Synthetic prequantum field theory in a cohesive homotopy topos

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Synthetic prequantum field theory in a cohesive homotopy topos
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The homotopy topos over the site of formal supermanifolds carries a progression of 12 idempotent adjoint (co-)monads. These allow to synthetically formulate varitional calculus of local Lagrangian field theory and its higher pre-quantization.
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please to an and with a 1 1 1 and the thing and it takes a limitation the things in particular for being a workshop where much of the notice that I want to use have actually been introduced this is rare for my experience all others runway into into saying what I wanna mean but quantum geometry of community in a moment said it refers to 1 of well-established German was introduced by solely on the in the seventies so use that much but I I do want use it here because it does make a point so what did it mean of the 20th century instead of this so the writer geometries does the confidence manifolds and I'm gonna let you can see from my title and make some connections with releasing the list probably will be the weather map and and 1 that I do wonder if this motivation partners is the 1st bought a stake things about our commits physics physics as you know this is what became a big thing smooth manifolds 0 represents space-time but they also represent face spaces that she wished Faisal's states of classical and With some extra bells and whistles quantum systems face basis known as and although it is in the twenties all the content of cotton John tree which is a generalization of Riemannian geometry also his conformity Transerv celebrity Riemannian geometry Romanian conformal complex but about what kind of excess structure that you can put on a smooth manifold and famously this is not the 100 sunny anniversary of this inside this in physics describes the feel gravity and another important ingredient is the president to surrender presenter was abundance the figure 5 among those with connections therefore they said they were wasn't to different things someone had it's it's these are these on mathematical incarnation of gage force charges famous directors president says that mechanic charge somewhere then the left-wing fear
81 principal bundle with connections in the complement charge get 1st choice of false charges this kind of at the level of space-time .period face basis and that the word pre-Columbian comes in it so my mom of connection if a space that lifts the simplistic form and this is what sort of called frequently quantum Crisp so needed pre-qualification of phase government double conversation offered in as opposed to a citizen from each
inquisition informed part serious of age parts of his relatives were frequent comes and I'm not gonna today what quantum physics for just about all be careful about the speed of order differential geometry with his Creek 1 mistake to think car so this is a fight over collection and then there is a In addition to Cobbtown on theory this general theory which is about finding characteristics of these 5 of connections the physics of the 10th century prices crimes physical in some towns much any of us want to recall Chen thunderstorms Siemens theory and the same is worse for those knowledge for those who don't I will not explain that his sister and his motivation and related to this Western awaiting for the points that cities are important important aspects of applying physics and the kind of Phillies incarnation of this plan not something happened it started in the 18 of the 27 favorites of happening now as we speak so this is really a particle physics here and now people thought it would be good to have something at Branford right side of the brain is 1 brand costing theory about the the sirens of this and we're concerned about some of these things so 1st of all so something happens here because had already admitted it just became noticed many fully in this country that spacetime is analyzed to see and to the higher super or before called sober damages up to play a role in single point less space cancers South coming in for important is grateful if that we take space and to be more influence all overflows the special case although the smooth group on the saw so there's a mathematical incarnation of this and this is what concerned about exercising these things to go in the right column here in the stock today so so the mathematical incognito what these things on their Super it .period Infiniti and are hopeful on the 3rd bottle on the future of the field complete isomerization of 100 disease things in other words privacy in the decisive airspace said If you wish she'd something manifold and we've put it off and make support this what you need to use from this and see us as you supers recently so I hadn't won on to gravity is is this really the keeps on this this avoided done yeah maybe with a bit of imagination but something important happens M gravity becomes higher dimensions of reality it's 1 of the name the nice thing about another part of Cinquanta geometry here is that it gives us a muted wait to see what this is a kind Georgia's the joint induced from a group like the pondering over the subgroups like spin group and you the bill spaces that locally modeled on the on the infinitive because it's Beazley's Heidemann severity just comes from using the Super Pungarayacu instead and looking at about the low-key modeled on these of the point Due to the tubers figure visitors turns out that these have these Subaru here intrinsically a higher form fields them and decided reform feels they are really to consider them globally there hired Europes which delivered Ohio kind of differential geometry which goes the strike on here so so there is this is something that should be called higher super cotton geometry I would say that about what that is a mathematics musician and hydrogen super-rich flex-fuel then no fundamental connections they go to so here we have charges like the magnetic charge of particles and so some other have part of replacement brains the things called bring charges in 1 of the bank's inside of the 90's was but then along Interstate really injustice you know on the abundance of connections they take millions in what is called In general commodities theories so the river by certain spectra and and there's little bells and whistles facilities up to a state and a grand commodity theories in the presence of the the connections on the bombers translates into the fact that this a differential commodity sectors and for this so I will give you week musician for what they it is see as a depression brought present ability fearing that will tell us but these are just those sheep I also suspect and the in the way we've already seen in various parts of the island but much of it will be using permit 1st but dropped the tangible To get twist which are cohesive this is where the work is of constant so there's a certain actually could put on your mind physique your spectra which ensures that all of them represent facilities listed denied the Frenchman ,comma so I'm lost 3 to their theory I have lots of significant released a list of the sensor mysterious also the higher hired in Trans-Am series here chance Einstein's theories that the plane neutral so 1 of them having it 1 of them is because there was no that the AKC models with a case of course referring to 2 months in or integrate them they were originally fine on an Infinity I was from Canada went into these initiative on higher stakes and they contend that I'm just mentioned his words will not mean much to anything that couldn't possibly want to Corsica model a model to be more strings lots of that the truce scare about this .period so these all come from From quadratic shifted forms this means also 72 summer series is important in the ongoing discussion of the 60 possible from a few theories and 11 transcends theory all this all these come from higher animals of the trend workers and it doesn't use this a string field 3 which is built by the same thing so I would have say anything about this matter for those who have ever heard these terms this is a motivation that this is what the technology that I'm trying to position on the right now is going to be about salt recommended something that I Infinity chance unintentional but you should really thing as being that the higher the height difference adulatory version of the original available and similarly for 4 WCW stop so what is all this this is clearly something you know if you believe that there is motivation for this kind of guy you for this but I think there is then then we do need the mathematics that does handle this the 20th century memories does not handle this anymore which is the cause of of much of the difficulty is that the people see because those inside using matrix Scotland for advance the knowledge but I think anyway so so this is kind of an inside joke writer clinic 20 1st
century this will have to be understood and develop standards for this what I'm going to talk about why would I thought others this you might just to just to maybe say will use of people already doing this really highlight something that is so latest some on million looks as as vivid in the brains of mathematicians and these days the 90's were somewhat different there than big mathematical problems here that the fizzes ran which which deserve whether medical attention 1 of them goes by the name image of status for those have who know these words so it's known that it's not that what is called everyone keeps the bring charges for this is that the big inside it's in the nineties and other people freed bring charges are in In Inc twisted effective and differential cases so there's some sheaf of Spectron represents twisted differential and K theory and it's important to use this to model of the charges of these brains and direct analogy with the magnetic charges here and it's known from kind of the physics law and that this has to be lifted 2 but this all of this should be if this test that was something was useful and 2 and 5 bring charges In got us some Jenna's commodity theory about the surrender saying this is an old problem that's kind of the well-defined question that find something hidden under certain transgression circle of reproduces this was closely what the severity of it so happens that it was the was the next 2 weeks in a lecture course is in Vienna Austria should interest and buying come to the end of next week so that evidently Institute and I'm just saying that to highlight mate but there's concrete of problems in this issue got me in all some people got the impression that entomologists interested in uh in abstract formulations of of geometry but that is not in the case of what I wanted to talk about today as the following so we saw privileges which was left column on them the right to be it's something like a higher frequency on the end user issue that I want highlight and insults doing this this is hopefully a kind of evidence already from the security is not feasible to do it in a bowl marked his tumultuous does not view possible and components started my 50th of 2 degree 3 Ford Nunavut so maybe 2 jurors has connections in compliance and all the definitions and all composers explored the just exponentially increase before you write any theorem you have the Phoenicians that spend pages of pages just possible what is needed need a faithful a good emphatic language synthetically so some abstract fear that doesn't exercise these things by the times for the building and which dust faithfully expert what these things would behave like says that you can prove the fears have to be proven without getting bogged down in just 2 choices of basis Saunders the series which I want briefly surveys turns out this is possible use infinity top office that are equipped With a progression if you wish this sequence all of them export a progression of the joint the model operated all of the witnesses and just a 2nd 1st of all year and and this is this is what gives to the this this progression and will secure the next board needs the names of so there was something I was suggested by the European Union Vontobel series called cohesive infinite vocal enough his infinite opposites but it's that we we do he was not convinced that thanks send etc and as so we we make we make .period on you know you have to choose someone I guess in my book I call difference the cohesive and but also the suppress freedom would be super Airways announced just the point is there will be not centered at very sympathetic of excellence and and was kind of surprising this is something I and look for this week we learned that we were trying to solve this problem at some point I was overlooked I can just do all these things that were really difficult to adjust to the asserted joint and then you know once I have this summer saying will lift the sick if maybe I can do more with more than so if that is the deal so that will visit this my motivation for today find synthetic language that allows us to go higher French ,comma legends differential geometry so salt those word of saying but all of a very concretely use the site in descends into the front of the Ottawa recalled in the Bundesliga matches at the beginning of the site for but not to worry differential geometry and if we do if Russia geometry and managed to prospect for the support what working on well it's very easy everything is modeled on a few things about movement for the modeled on the spaces so this is what we will we take here this was a very wide is the erratic current space before movement oppose those that are already in use the canoe routes objects are ends for various and the Memphis movements which is this the supermodel species of fines if you wish for overseas of all we can to the guidance of different Moffat who bought his the violence a what could table could also take people like to take all manifold them yet we were just giving 1 side there are many different versions of it inside and out and so on so we I want to find out something that is called or that underscore called former MEP smooth manifolds can formal criteria space is what is meant by this will use it progressing as it turns out that the fund the takes smooth manifold to its real smooth functions regarded as an ordinary algebra commutative algebra of this should fully faithful so you can have characterized manifolds by this Consent offered by which fear is lower Kansas to and say and is as good a good dividend for the former schemes within the state willingness just take for either have infinitesimal thing of these infants and being found on a piece of Florida space that is so small that some fine upon these functions which he vanished so it's alright objects as the objects and former Carter artists are in times the use my generic symbol for informal disk infinitesimal think something that is appointed the former thinking and it's defined by the following that say regardless of functions some of the finer despair free-kick defined it to be detained product of the real smooth functions as an ordinary Arledge well-attended or are something on the form of an underlying vector spaces of this form but where the is fundamental and important the
portent for the weekend this you can filter this and to look at a hotel or variants of this but for undermining the case where this some end some national such that every not for every element the sum and substance of case and power is 0 :colon the original you could call this a local arts and on Gibraltar are these we it's really on in this because customers they'll introduce this and that it was holding so this is the light on us Muskoka and Bolivia is available the other emerge as as it the local party so this is something of this these things as being functions on point and over there 1st orders of some can expand and the space of their funds some disease so small that some the the physics the way I was taught to coaches and referees quarters becomes a future with some finite politics should become 0 right around the world over you yes yet another way to send so this is how to find the former captains and then there's of course isn't getting here which as regards Indian space having no information with again it will become a report but as you can is a check this score reflected so my joints always go this way lifted on sample book writer John and just for the sake of it since calling for much happiness the audience of also consider the simple case super former Cartesian spaces where just the same thing I just enter allow the side was to be suitable to welcome you to the institute granite and committed 7 into right-center and I simply continue this latest still be ornery ring of those who functions on our end but not as a was that is a lot to be a support system for listing have something that will be cut important here is that there is of course the wasn't getting here which simply that everything into the even greater peace and this is actually to reflections and with the what country tastings of evolving body of evidence that the even former Peace yes salute will come here and if you wish of course at this point which is reflected his ability to this society values are not I applied the chief infinity from was discussed in the pictures at the beginning of the series to define the infinity of losses of support the French jumped call on the French and you saw the sign on the very last Saudis 50 sheets of the .period maybe died in pretty much hesitation this wasn't worth a few times so this is the same thing as what I went through all called Infinity group I know there is there and it seems to be reported in the habit of saying spaces for this some of the speakers before me roads basis for this I'd underwater cautioned about this and you these questions came up he got to the point of thing of this is for the Commodore thing because there will be lots of other spaces appearing Exeter metric mindful going the space this is really a applying a trick which ones should be fully hopefully where relocated topological spaces in the simplest localization of the week ,comma equivalent salt cover trick that allows users think what if reports is being an localization of public spaces but what is really important that at this point because Georgia is concerned there is no geometry here he said this to the body contended discrete group or it's the discrete there's no geometry here the and not topological group at so you can also Minnesota right so this is also the same as can also take some pleasure always you wish you can renewed restricted gun complexes Israeli category theory kind complexes localized at the time at the moment is that you know you conditional these at the home of a case of this is kind of our base in would clip this systematic structure and the way we do as recently considered my fatigue with a permit tries of the smooth guys by the front door .period perspective which I is in this context discovers that only to to say much about the sale of space have 1 2 3 4 this Nunavut space shaves Infinity on current space this is what I call the rich and resolve it asked you invite you to think about as being this smooth infinitive ports particularly group points they are full subject to ,comma 1 category of this year's it's our for instance in a simplicial good qualities simplicity sorry there is not yet supposedly get there so you know we we will not do the same thing going so can do the same thing on formal conclusions there says these are now smoothed the son Finnair was equipped with a dramatic structure that is seen by testing from Gulf .period was with former captain spaces so they will look like former Infiniti Q this wanderlust engage this is what is there little sokaiya was was 1 of the 1st published as a faithful models for the viewers Symphony differential geometry so this is kind of infinity stand 1 for infinity synthetic geometry and then we can wants 1 war which also has a vague precursors of religious fervor anyway so what he did to ride on these things big deal will be to see that the joints between them are actually all we need to know about the super former parties spaces so this is now not you know I just keep getting these adjectives used thing of it is being so former schools changing reports Sullivan the Saddam's was on the preacher of categories they use adorned quadruple slaying delinquent toppled by a live like comic sense of focus between these issues categories and the thing 126 sector the citing onto the stage this year of which of these do past the sheets and it turns out for the 1st case all of them actually do which is which is a strong statement about this proposal achieves this semester the the O'Donnell little bit here for this aglow with such a fund that has very efficient almost since this is terminal Jake this justification the point the .period on the point means that we forget kind of this new structure we forget how the test or Infinity was on Hamilton bought into them we just Mortimer appointed them so this is just forgetting this new structure to get in on the underlying Infiniti Q yes you lose a lot of those who is he if I have to regroup because of the you hold half of the year by the founder of points the reports which which showed that ecology boarded say it's system of 2 to manifold would you take it to be the chief that of reports that reached destined for you to each and assigns the group .period witches see Infiniti you command you want them to do more to "quotation mark lost and this is a regular review of her interview with you have to have Congress of multiple cases against this was
looking for conservation and of the geometric objects in here the geometric Infinity Group was supposed to promote the use of these years for reasons inside here in my head I wanna get into this time by half in the north to see big diagram that filters this all the stuff that sits and lots of classical stuff you find is fully fit for its use of kerosene heaters this year the concentration levels that many people are are into the new but it 1 footing broadening specific perspective you that before we focus on 1 of the separate away want to concentrate in the end but which do not have as nice which do not form an ice skater with a focus on this very nice category I said my theory in here I find not to everything in here and then in each particular case and the end of check any given construction she lands in 1 of these circuit which I think that's the way to go otherwise you if you restrict itself to only use the mysterious was the way goodies .period of introducing so this is in there and so this fund has is every this might have been mentioned that some victims of so this has is left exactly after joined Witcher of with an indebted Libby :colon however Dias because what does it do it takes an affinity robot and
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constant on the site but the by interpretation so will assign the same value to each party faced about that thing of the cut is space is being in the points every map into a robot adjustment everywhere from a contusion space into a report that has to be constant for this this equipped in Fiji with discreet smooth such a structure the only with maps and then marked the constable and I'm not turns out due to the fact that we do have suggesting this dust so this is what you have every this affront left joint here which had reserve products Alexia and and this is something very special and let be this my 1st of monocle despite and I put example here salutes the status saying what's on these things don't so there will also be somebody's served exorcist with manifold for instance regarded as sitting in schools Infinity reports under the Soviets standard unit I'm betting at my kind of fortunate but but I can do this and then sold it uses a online is approved as universal the source from which effectively resourceful a shame the measurement candor and a few more things very so there's always somewhat type this produces the fundamental infinity pool .period of so if you wish this is that this is the singular simply complex although underlying topological spaces make regarded as representing gone complex and Infiniti Global is what's called Pine Finnerty the Tahoe more of the type font .period since scheme which in our case the manifolds to its hallmark of is something 1 1 it's approved and the figure this is our joint if you think about it gives us already has a synthetic version of guy with consistently let's agree needs locally Constance text to to the whole development bill passed on to her was the end of this 1 1 more joint here such as the of business turns out to be fully faithful and there's 1 more joint here which is set for the governor's being a crippling staff of the coldest construction firm song so what does that mean in order to analyze these things and is very small operators come and see what I really want working this all the way in here is that big infinity doubles that I want to talk about so I always call this age and this is the home former generals commodity-rich big ages reminder of the college there so I do what know how I was going to replace all these adoptions ago between different was as just a morphisms all my mother won categories its form this way I'm all right so we can go down yen smooth Infinity reports since the since this is reflected in these ways I'm going I'm going to consider taking 1st the global sections and then reinventing discreetly so this is just the the underlying discrete infinity report but thought of as sitting in here and this canonical bed this is the name and not just having local this flat 4 this is called flat where is another example take there will be lots of books example systems said genially growth or simplicial legal if you wish then then again in the near term on the phone and then maps to this day in time and in the opening of the the group so that the deal paying over ruble object in charge of the top this that classifies Takefuji principal bundle so this is a principal bundle is classified as a principal bundle and then you have this flat operation here conform flat G and since it's is not called 1 of the cases canonical forgetful meant to BG and you find that lifts here there equivalent to flap connections on the jeep riddled by flat connection this was called flattered since modernize texts of fruits of honest 6 of low consists of the things 1 can yourself so this the beginning alliances that this is a joint action college interesting information so that a given name to the other 1 for the other 1 is read we take global stations but then reinvent call discreetly this seems to be an exotic operation I'll call the shots just because it runs on flat lately and then shot had assumed to have a nice invitation to suppose suppose X is is a 0 truncated chief except in turn to Austin with affiliated with those deposits and just plain sheets on cots space regardless of fully fit for sitting in the Infiniti sheets and cuts rates many others factorization you have the the unit of so this start exercising weird but here's the thing consider its army from obsessing about this perspective confidence image factorization with Victor this through an MP followed by Montoya turns off some article the shot 1 was the 1st political station is image someone effects this is presented the logic of space completion space underlying facts so logic of spaces and was introduced Osorio exterior this budget wouldn't be willing theology today they generally smooth manifolds and therefore what this is saying in the logic of states are precisely the concrete sheets in here and those that are separated appreciation for the Cheney operator shot so just mentioned is that we see our home in his diocese begin to see sexual metaphor geometry here and now we have of course 1 1 so we can also go down we can also got on the plane Finnerty and then we met discreetly and this after a long discussion of my mature enough corn and shake it was a "quotation mark shape because as you already saw he had it sends an object to its shape in the sense of shape to it's a less so for instance a back to this example if you have the looking over legal the moralistic of students will bundles and shape of it it's an ordinary Infiniti will put it on their what because constantly reinvented this turns out to be BG so with all the boldface my boldface to indicate that this extra structure this is the smooth version and this is the ordinary classified space of geniuses topological space of 2 we commodity whose breast flat PGA just emphasis fled PGA is what some which would call Kojima all these things to on all the bodies joints and Yeltsin solid wires used to be in the world yeah maybe but but this is the yachts along with them this season although he did not know what that you are here and I thought This is the best thing this this made everything industry that always comes about with this winter a geometric innovation so generally have a simplicial manifold shape of which will be the fact nor folded the Fed's interest realization as almost so the figure dissatisfaction during shows that this Sasanoa something more different the commodity and this will be 1 of the major exploded um let's may be completely with and he also I don't know think computers to the squares if 1 wishes and and a lot of people continue to give names for this said that it has indicated from this further a joint you have to get no further from so we get the embedding it's just more than into those and also a former thickening and that that's a reflection to this and what does it do well it's that's the very soul of Saigon offensive this for fantasy and that I'm usually joint dues from the centerline and I'll give them names so in the in the same way the leftmost 1 it appears I call Rumor read this would be the reduction operation yet the right on this 1 comes from the top of what is it doing so if you have a former thinking a former manifold then this is introduced pot In sense of satellite by Georgia
you you it the get the object was a ring of functions the simmering of fighters would not the the book and as joint which comes from these 2 the joint fantasy in which you not to use the kind of dual rotation a call in and in what is the classical then is to issue an accent larger which is called the drumstick effects another way of saying is this is the the quashing of the 2 projections of the former neighborhood of the the effects of that was comes down to all this is kind of a man making citizens not supposed be and so the data would we will use all of them all others on it cannot it follows from this well I mean this is a bit of effort by the vicious lies over in X then this will be the category of PTE over X for infinity sex so all logic there will be bundled Zovirax equipped with a stockpile of the jet partner that defines a partial freshly created business at the end of the tall relay the field theory comes in we'll be able to do variation calculus just just using nonlinear please him so she just look at you another argument if you'd like to consider just acquires the Korean on the wrong sex now that the models on the original scheme that kind linear Haiti's population wanted some serious variation garrison in London alone it's all that this is a further further the joint which I call but I'm not going to talk about this is that it it's important for young some analysts and these names and then here the same thing so we get so we get these 2 ways so 1st of all former manner .period editors abominable the only peace and this to ways to projecting that take the belonging body and to take the firm make peace on and off looking for some days here maybe this will cause some Oregon I I call them I decided to call this guy traceable like body like because it produces symbol for bosons environment I tried so they have access superstar swoops over manifold then then this thing will be the underlying and body will hold the wasn't where's and if made this choice than the left 1 it produces even number of fermions himself so if you didn't do not buy double error this the former space former space it also even so you don't you don't throw away the the law upgraded guys but you keep just stare even possibly think that the even greater and then it it has won 4 of their joint which for reasons that I want to what called the only visitors since were riveted futures doesn't actually we this and that if you want a while ago account at 212 and my my abstracts so what we're really doing is starting that almost all much more of this there an initial Johnson sovereign everything that was to take the that model constant on the initial technical modifications but there were on the .period very joined this guy is flat this guy's job meaning its and his idempotent disease of faithfully support my these things all faithfully and so we get all these modest income was idempotent so we can ask is shot the point again the point that it is it turns out Ashley Sharples empty is also and so on Sundays are included these are included these are included in the century just warning kind of snow and this properly graceful exit you notice also distributed junction and if they come to arrested this just some attention ended with multiple heart promise I mean this is maybe the the thing where 1 has to work the rest the the rest is just making the right observations but the point is that when emphasizes which is lot of it is that this was surprising to me you cannot ask while you know this fate if you if you take a random the phantoms you will notice it does not have many more joins this way beyond the 1st 2 years these are strong conditions on if future was to have this long sequence of joint North like having a joint codify shifted up a gunfight continued to until but after results of its this next 1 year resulted in the theater next to a strong start and end of you could say Well if if the comics were working in has the strong extraction administered estimated service must not use the whole lot about what we actually doing components in this thing so there's that using just the joins you can actually do differential geometry and then there is the running claimed that I want to make it you can actually do a whole lot of just 2 dissident residents and lifted off to infinity and so do want close now by in on the last part of all wanna say how this morning it some serious works for this book still do With the synthetic differential commodity using just this a joint in this box although synthetic but well I would call a synthetic differential geometry would of course is already this is use much quieter very content with what I'm doing here will subsume this but let eliminated made emphasized that will introduce Cotton geometry synthetic it's will find the funds the Thailand's physics Texas Intel manifolds and we will be able to equip them with conformal Romanian Belarus structure super confident and if time permits but probably won't the I should you not to come back to the the 1st words my abstract on this boss if time permits will speak about doing synthetic on just main facts about synthetic variations catalysts on jet bundles but we cannot do it in preponderance waste will actually be since it so honorary should get is kind of the mathematical of classical field theory but since I won the forms but their depression "quotation mark find ways this will be his distributed this free quantum field theory did you see in this so decided that the 1st cruise aboard want continual thing would be just the 1st tee statements in the unlikely event that I'll still have time after that time just for entertainment purposes and is in this context it might find some friends also a some nice geologists sector could system say something about something of substance effects kind of need to come that's that starts here yeah I was something with this in mind and it isn't isn't this mainstay the way I'm saying now unfortunate incident that in quite a myself this formed by Bocanegra because and focus so this is 1 of the was very fond of the state sodomy College the differential differential Bronner president sought bronze received for readers and her ability to 0 so the brunt of the media films that recorded the region last month here in this and understand this is given by MEPs and some spectrum and the question is who is that under the age of this for differential commodity if you know 1 of Article 1 of dozens of questions if you don't know about the vertical largely because they weren't saying is the quickest easy definition and then just go from there so this was approved last year by Baltika we both Thomas Nicholas Indonesia In and the times such as the following we all know just enough this limited space available to try to get it
to do so would consider now that the it's alright Ch for the tendency for policy in your sense of tens non-communicable is that OK override I forget which edition you use medicine different and so far at 1st the 1st years of his Palmer objects optimist saw firsthand observation is this is again cohesive if if if we start any of these proposals inflate plight th of it then the the result would have the same structure is in view recent inlets yes I'm calling this increase of foreign destruction and who have these extra incentive things with this fully faithfulness to the structural cohesion a what that bubbles with the structure whose job is to they what and was this is for the federal then is equivalent to this being fully fit for the Bulls soul icon official Bosco he says is the challenger metamorphosing has the properties that the inverse image fully faithful has a further lettered on the floor products and direct images of from right an online publishers want Libya headquartered in Cyprus from the start and then there was summoned to the Johnson that admitted this has been considered by Libya and he called equities it was picked up by then investors existential policy goal differential cohesion 1 way to motivate this is so this cohesion contradictory thing of this call was as knowing what it's how it's pointing to get a hole in an open bald appointing smoothly together is exhibited by the shapers contracts the way 1 can show this the around 600 is like infinitesimal contracts away infinitesimally close .period In this sense this is too fresh clean and in this article on last Super differential focus yeah sorry system noted miniatures another terminology so the Department must make and consider for the beginning just a spectral all the points suggests a sheaf of spectrum over Cortines spaces it's called this evening for the theorem effectively says they're any such so these are these cohesive spectra are the differential commodities what is the falling 1 shows that if you take any such guidance and then look at them what its projections are fine art but these despair of for this strip along joint and have in these projects fit into a big diagram and you've got a desire must assess the diagram hexagonal diagram that people use to write on 2 excellent time differential commodities so yes has 2 aspects of this big tax among so 1st of all I did his what works cited the ship consider the shape Of the get an ordinary spectral spectrum kind of this issue the .period constantly that is a constant for spectrum Nokia conjugal Specter and this is the underlying is the underlying commodity generalized commodity fearing Water no more differentials of I don't want not because of the use of all the time we can't afford for instance the leading the delay complex standing colleges regard as a should spectrum Davidian complex and then if you do a shape of it you get a H z right you find that it's order into the local
militias In this sense the accord a difference refinement You can take you can take the sheaf of the stack effect the benefits connection Stewart said Infinity Group completions with the show it gives a sheaf of spectrum it's it's safe for the KU the ordinary case here spectrum In this sense we are in favor of completion under direct some or all of the stack the smallest sort of Infinity would affect about his condition is the French refinement of KU and so
forth and so it was nice 1 1 can 1 can see what can also form the coal-fired reflected because of political fled boy subsidies meditation forcing the core fiber or from fled the From the unit of this monitor was to eat this turns out to be the home of the courage of forms the French waxed coefficients ,comma being in the radical my so feel free to take ordinary vertical this comes out as being the sheaf of closed forms in given degree the ordinary sheaf of schools closed for forms to put in Kayseri uniforms or even degrees created by the generator shooting take elliptical you something wild and so forth so there is nothing we Freedom Circle Fiagril flatfish should look at the fiber of shared some illegal the State Bar of the definable modified of course all of people who said he for these other things these the differential Korzhakov's underlying bond lifter which is trivial he said not to be the Pacific globally defined clearly defined connections union officials from 1 to get a feel for what it has recorded this comes out to be that same complex to depression forms you know and law degree 1 degree northern Europe curvature and then you get the canonical met here this comes out of the Doron differential again on ordinary colleges is the ramifications in generally give some of that behaves like a drum fresh 40 cents sees another theory the approved of these so that's a strictly from using using nothing about what he is us just that joins the fundamental theorem of of Goodlettsville yeah I think so sold you know for for generalized civilian forms in the sense that they exist the map they exist and have been duration from 0 to 1 from the mapping stake from are already line which into into the scourge of forms disclose forms check to the coefficients although the connection forms and money greener this behaves like in so 1 can construct this African the map exists is the the statement exists canonically and it satisfies the condition that if you precomposition D so if you go this way and that integrates then the result is the difference between evaluating at 0 and won the difference taking the suspected being instructions spectra and again I'm not running to the boarding and part of the series if you don't put in in the fresher commodity this Council is being on the integration of different forms in the order affirming calculus of financier fear of Kansas but you can put in in the 1st recall what is amending on non-elected the final theorem customs yeah that's what I was fits on this board for synthetic differential coal mines 16 1 can also if we don't take our spectrum look in the point but over peak of care you think of some some and we get twisted differential just for free but this incident so this issue solved in order to solved a problem that's what it wanted the solves the problem was it was raised by Siemens and some of them in 2008 in so this increases again this was not his was not for these authors did not introduce this because they wanted to play the since they wanted to solve concrete problems and that will open the fragile collision theory and it turns out before my eyes at extra medication and drops of water and there's a lot of it says something about a synthetic differential geometry for time so suffix existing Sigma in an hour so so now I'm I'm working young ages 9 and context and then consider the base change depends on the depend corrupt conduct based message if you wish slice or Sigma flies over it's the wrong thing so then from from the unit of the in Mona we get this a joint Tripoli the unit I should call you tell him for Cigna it become an addition put back is a writer joint Peter in Sigma before so the point is that we have this got construction and now we have we have hormone after all ,comma the unit and coded messages you can see here a week displaying destruction from thanks from co-filers mind putting back and forth among these units and go units and there is of course the left joint here which could be called to commentary and so this induces again I'll always transfer back to monitor suggestions to monitor this induces and a joint pair of 1 thing :colon on the slice of stigma and I call this the Infiniti Sigma and James infinitely for reasons that will become
clear just saying this would be just as will be former so there's no from the slice of segment to itself right so so this goes 1st down with the left a joint and then back and the other 1 Gophers down the writer John for the Jets we need for the race calculus is that is the statement that we will need for the differential geometry of manifolds he observed the fact that the Infiniti signal Sigma itself Is already almost method is the former despondent so it can only comes amid Delta Sigma is a bundle over Sigma and its fiber is the four-minute its Oregon .period is the former neighborhood at that point and and using this weekend something lucrative song file of the and then we also observed it in the forest and is something that I learned from the bottom of consideration of the Rosenberg on 1 communal stacks in very different language you characters itself only tonnage if 1 online for settling this paper is just what this just 3 of the joints that I'm using him in that very nice was observed the 100 Georgian and solid this site remarks saying saying If you have a map in such a context but between 2 spaces then you not consider its nest the nationalities square ball Of the immunity from From this state-funded unit you can ask me cannot ask that this is a point of exit on his appointment this being a pullback means that this map formerly top this is you can take this as being a maximization of formerly in the sense of August when under reality way because somebody with me the correctly for this 1 can 1 can check with consider sit up former exodus for what old maps should be in the mountains this dissatisfied this but so this is a good exposition that part of the stimulus if you actually put into a smooth manifolds your to attesting gender find it then then these magically come artists and local diffeomorphisms piece of the correct form comments now we have this I'm sweating and making something wonderful on article so so using this we have now we have now but definitions of Of the task said given V group object the group objects to Infinity Group edge performance most Infinity groups liquidity the leave for instance it I'm writing V Yuri supposed to think of it as being for it's just a vector spaces a tentative researcher and a model manifolds on this vector space but it could be any group then the necessary then the manifold this is not some of the internal definition this comes out externally as being at the top of infinity but some it is internal logically we just think of everything is being sets group structures of the manifold is certain it's an ax it could out last summer that the 1 at the an effective activism and the inflatable sense all some you such that this is a time for many time this action does the victory of the cover by old maps but then we wanna say this is all locally equivalent to a fixed visa we just think that you're looks locally like this retirement from you back to the it's a corresponds if you wish the transfers the structure on the the local talent search the to the local tendons of acts so the detectors as ardent as my definition than the sickness or injury to the back of your we'll get real the cotton geometry in this little square appeared on just a 2nd somewhat what I do need to extracted a conduit which I didn't do not approve it is sufficient to get frame 1 of which I can reduce the structure and business it's not true abide said it's a simple dress so many posing as this proves scholars kind of the floor they so using my the Torres arguments and stuff you know you can prove the following year equally propositions little exercise only for people and something a Solomon you'd you check that the if you have a group object and it's it's free money for the group of object Pierce canonically need Kelly trivialized by left translation point of translation we just in faces 17 Group stack this can be there will be tricking components but you can just synthetically deduces now that was fiber and that so the fiber the typical finals this trivializes former despite the whose fiber is what I would call DVU just a former neighborhood of the neutral the neutral element .period In view so this is the 1st Amendment and indeed it now this is not sufficient to transfer this X X 1 half of agenda former despite the weather will be Ivan locally over you trivia from this 1 and that's another thing I'm interested in
Infanta was every 5 abundant sexually associated salt so it follows that for every for every the manifold via tirelessly for infinity stack then then its former this fund X and follow this plan is it said the VP final 1 definitive fallible and if you wish associated so there's a fear of Prince through violence and fear the
bonds infant was assorted wasn't forced to the sort associated to a one-to-one ecology as the principal behind where GOP B I take to be and stand trial automorphism group of DVD linear motions tried to this will work the jet version you take all forms the principal and principle Infiniti brand In the end is a particle the frame by frame of eggs and then from there we get ,comma geometry and from there it's easy money of the frame under the can also ask for any group for more than from any group infringement due to GOV and can lift the groups and that the Montreal senators maybe to really took out a Georgia you wanted to toss and free structures so you need to do 1 more thing you need to reduce the structure moves and then say that again form enabled wise that Tauzin free former neighborhood that trivialized but you realize with respect to this true position this turns out to be this turns out to give everything that was imminent In an image of Superman before it turns out that the creation of motion of what's called 1111 severity is equivalent to taking the right the year for certain super infringing rodents canonically defined and then just looking at just the tossing free 11 measure cotton gin this this turns out to be give the level from efforts to solve the careers of motion some of program the find this endpoint asserted in his nose and distributed OK so I guess a lot of times around her but I'll just keep going until you stop me saw yelling so just greatly yeah we do jet geometry and and yelling adjust its takes 2 minutes to fill the sports and it's been taken thinks abundant over some signal and thing of this is the field bundles of what would will happen is like this sort of I'm 1 of we'll put out of entirely into the slice for this work over space-time signal or willfully and Sigma and your unlocking the two-finger flick follows his effort began as a guy in the slightest Sigma to regarded by identity met in the slice of this that or object in the sliced salt and that you will not be a section of section of the spun left and then if we reaction destination view 1st book any movement before the sex was sold section of a given by this is how you ties contrition physics so we think of besides being a field configuration I take after being the bundle offered our ancient has something this will be this would be a few coverage gravity and so forth and so this is a standard stuff is what which is a positive thing of this staff but now we can do the falling stock so in age we have different commodity here in a Gerets agency ,comma won't be cohesive anymore but we can kind of compare so we can do is now we have the canonical map that shift everything up to a differential equations so so we can all take a guy in a ditch and we got is forming the final the trivial but Sigma endemic front 2 0 2 regardless of the trivial Potter friendly creation Over signal by Israeli this comes from from the back theorem for this this is really defined as being there the more categorized as Jekyll 1 at then by bacteria noses of slice so what do is we we push forward on understanding of the same thing as producing freed friendly creations we just forgot the bundle is being the differential equation which is trivial such all sections of the bond solutions so this is a way to Kennedy and that or of context nite toupees and now are back we have we splitting yeah there is horizontal splitting 1 can defined as I looked at at enough time to service this so you can take orders commander theory down there In accordance Mexico which shifted up this PD context regarded now over Sigma there's economic projections to its horizontal piece the quality age the horizontal pieces roughly that which is
actually seen by sections of this would have the structure the opulent PDE theory but if you put back along sections part of the structure will disappear because the sections would only see a horizontal structure the sentiment of just so we
project on that piece that will be seen when intelligence sections and then it follows that this is projection in which 1 can define and then and it turns out and this is expected to be in the 1st 6 6 is a thing of the nose and you can exercise field theory deflects all cellular fuel bundle know we have a map but we have designed the more categories have a map to the age but this mapping the I would more category between 2 free guys make Libya a Kleisterlee Seville be mapped out of the jet Bond this it be a map in H of the jet of this spring or differential coefficients and these are precisely the Lagrangian density the grand Indians the charge differential Florence 1 jet next now the fresh reforms tree quantized to differential co-signers and some so this will be a Lagrangian density which which defines which consisting of the finest of physical theory and then we have the courage and that this was this 1 here remember this stand a generalized bonded with connection to its curvature and now we have to kind of the horizontal part of the scourge of that gets gets us to the horizontal part of these differential forms so this is the provision for a fresh reforms horizontal the debt problem in front of this is that this will be the day this is the oil duration the relative it comes out as being the racial derivative of this Lagrangian when he was at the fact that of the FBI complex structure and it plans to prove this is kind it's kind of a properly adapted to jet bombers and areas for this ,comma said can then is a like that at the very edge of L and villages others hope the L is 1 Lagrange form I mean if you feed in each we ordinary differential colleges and agree this comes on of ordinary on Lagrange form in the standard textbooks and then it turns out forming fibers here this thing's gone the year this year recalled uses the shell this is the 1st is not object in the the find some partial adversely creation on sick mind this turns out to be on the ground please of motion that that France's associated to a given Lagrangian density so what you have as you can and well the section here it is a pity that maps of the supplanted distributor solutions these are the classical solutions soldiers Kansas G X and not just using the jet Colorado amusing that know what of traffic commodities and that their competitors and again the same as if you put on a illegal miners comes out is no ordinary story pre contest if you put in the frigid furious something more interesting ,comma the and so for them and can do the trick .period face the eye and I guess I have adjusted 1 minute it is a one-minute you say stop now on I they something in time is that there's a nice finish Argentine palatable take a take an accident in a cohesive enough fall in the differential equations Thomas and he can make following definitions right she's inclined I mean that is what I mean how find to be the slice over X but on the on the formerly this before .period subcategory of size on those maps that are formally so this is like and in the summer .period context discussion of that of the thought of Boston the ridge assuming there's no fine condition my fibers some of the reflective and call reflected by the litigation the struggled with someone can prove fueling exercise support his action with affect arrived on proves that this is a topless 1 needs so we can think of the guys and has been chief of acts and I of the following supposed to move them into the creek nice edition so because we have a map now from X and you this tour To the discrete image of this small affinity group or swallowed evidence with some someone just to make it an object in a lot of then you know where here theirs this the univalent universe you can I'm investor just this is really start writing any this discussion he observed the universe fibration for the connected components hit back in the sixties thing so this is the input ahead on here is a that in the direct some of B or lots of 400 times as In this the diary some of what proteins Ashmont the treaty was known in the 60 so we can put this us back forms here and I'm and claiming that this would in this promise effectively this will realize they said being a locally constant infinity that on acts as being so are widely distorted that it will be in here but you just acted like this so his cash into this now I don't have time minus -minus rights or so this will be actually it 1 1 can show from just federal factorizing and using personal but this will be a stack of rocks and then you see is a beauty or 1 of the beauties values use that Johnson between this empire you and locally comes constant 6 on acts left a dawn-to-dusk aspire affinity that Parliament that from the expert erase anything that have to be mindful can be In the stack and highest salt so we learned that we don't have one-liners that locally concentrated section acts are you know give us a lot to be tired of X and in that they're the kind of committee permutation representations if you wish all the time a multiple of X classifies no Yukon within you for your patience patience and time all right here in this fall in with all the pieces of his work Eurosport which it fears you so you will have I always knew that the he was Jonathan thankful request so the way I set it up this is missed this disk just the BST part tried that judge words and to get it to get the just this technology in the north on this you would have to replace Europe repressor contusions bases by derived genes this which is brother straightforward and 1 has to be a naked below careful to have them so be cohesive but then it just goes through and then yes then um then the infinitesimal version there's a lot of voters over the differentiation and taking these guys and need a version will be reviewed here because of you it was the single most of the characters hold on for on a minute in the symmetry protected phases and topological yeah I think so yes so some particularly this is where this at this time it's freedom will catering by think what seems to be most interesting to me is that when the recent research into which he said it was Becker for me the 1st and he he he claims he claims in his original article that hideout is a W models were given legal genes that they actually justify this image protected the movement and what kind of curious for me as I was interested I was I'm using this as a consumer analysts ascribed super P brand screens for tube appearance and his kind of claiming that the same mathematics and or the same broad administrative control system introverted phase of medals but I have to say that when I look at is out of the sea that he claims this undoubtedly C the the process but anyway would be interested you the fact that these days and what you have yeah so yes so that some the the point of setting this up for us was that we wanted to to have a classic of your theory or program 3 kind of D transgressed all core mentions this is what happens in Column a 0 on of signal but it but it it keeps going down that next to choose a cautious office To them for a boundary of Sigma inside signal and then just put that boundary and then you need to adapt in note of horizontal at in in a bit more will become horizontal distance testing fuel stations and then you know you get other jobs here which I called the posture of well and then you can do same diagram and now you get them then you get the supply could you get the Midas synthetic forms on the core phase phase which which which I was so common called the priest inflected Indonesian transgressed back to go to major 0 these will become the subtracting the canonical pilots records back extraction phase you can see this in the notes if you got a copy of the the nozzle circulating they have made all use of new colleagues have yes so this was a big motivation for us to see this as gap or this you know there was this big breakthrough with numerous political what is left of that quantized losing a few theories on on on it not we know what it means to them and categorically but then this is gap that it wasn't known you know the wafers has produced few appears as always by conversation from a Lagrangian but there was no formalism that would give this extended Contra 3 from integrating another was a gap that the questions that just happened corners 0 but we not that the output if he had been in full coordination and categories so this the motivation you read this this sets up the followers of cleansing and frequent physics that goes all all the way down to fluke ornament and I have a link to an article when and this is the work of employs West get showered seems to be possible 2 quantities but proportions 1 to extend the but this is I think is 1 of the big question that you know that some people thing about this inventory this thing about this and and maybe maybe if I wanted to do 1 thing is I wanted to married to a group of 5 portable serious that there's this this is a big old mathematical problem a few which which was there is something to say about and if 1 could make progress with this thing huge impact on people don't actually care about such but about physics