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3/3 Knot contact homology, Chern-Simons theory, and topological string

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Automatisierte Medienanalyse

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a a rule a no and when you think you're in love so around so I'm going to continue this the series of talks today there is very little difference I want to talk about how this small country commodities related to some itself of the physics and so I will have to talk a little bit about a little bit about physics and there will be kind of sketchy and imprecise and so on so many of them in the human spirit of and falls but but anyway hope it will be interesting and it would be Canterbury brief but but the 1st thing I want to continue from masters remembrance that's what we did the 1 calculations so sorry if you took the I'm not so there was just a moment moment than we actually looked at the it's called ,comma flounder sitting inside this unit Connally Unit co-defendant bundle Austria which we altered was just a quick to 1 space arrest so and this was a mail the only can literally really carried out but there we could draw huge memory could draw the from the and was some kind of horrors also picture with it if it looked like that and that there was somehow these 4 the sonnets which was news just recollections of courses in understandable to anyone reading this in less time we could find this for home off a cardinal morphing beasts using fell trees and as there were 2 generators for these the and I'm sorry that I have 15 wealthier than responsive to generate the same category 1 and "quotation mark agreed to end and that and the Basra was just the following that the EU was equals 0 and the was equal to 1 liners into the slices into the pit of stew Peter the accidently so where where they remember the coefficients Remo somehow to the accede to the P and Q which was encoding the this existed only chewed on the on the call normal torus peace Meridian and Julius the class for the SCO so this is kind a relative who won the Eclipse it's up to now we 1st look there the special case Reid said so and then there was also the augmentation calling on the limitation of polynomial this year was just equal to this expression think that now let's put Q equals 1 years and then that ornamentation if we restrict disorientation belonging to Q equals 1 then what we get this one-liners into the explanation to the the goes to the it's consistently which is equal to 1 one-liners into the X 1 legitimately in this actually no accidents so or so it turns out that the this 2 factors divides augmentation polynomial of ending so I want to get it right to show and it gives you this summer are you using using some Standard property of it's as if the package is to 1 yeah right exactly as associations sometimes I should state and probably the seriousness of their own so frantic the orientation polynomial specialized Stewart was 1 is this providers one-liners CTX bomb went so why is that so so inside and these comes from and is so so the protocols for commodities and absent in this the in the picture right here so much like we define differential in this area and conduct toward the day you can also define a chain that so in this case we have slammed the cake sitting inside his use star or 3 and at end advances the idea boundary although there safely ,comma where the call normal seats inside the store to store at 3 in the sky is expected this summer are important for this sort of thing then this MK actually induces a chain it's a long way from the now all of the unknown to the novell this was official in so that the integers that counts where where Voinovich's if I want count epsilon operate caught this is equal to account for all modernize bases which estimated indoor like this have a positive punches at 3 according then that these goes down in the boundary plans on health care so L so what I would want to do is I want to check that this is a chain from the chain that come from users of the compactness result namely an and doing but the White Weiss chain sold so what what you need to know is that that these actions are account it so I write this standards may be as for later but this 0 this where right the posts is mentioned as equal
citizens did show such things but now if you think about instead looking at the modernize base of the equals 1 such things so then its boundary so the boundary of this thing it's exactly 2 11 buildings which on the top of the league was 1 these and on the bottom of the 2nd level is indeed was 0 this now that means the that's this is a chain replicas of the boundary of this one-dimensional space no consists of such things and they they're exactly that the 2nd executive with the things that contribute to this confide compulsory did is therefore and this is a change so this is this is an augmentation What does it down along the on the on the homology variables were ontology variables so the only 1 you variables surviving sp Annex in only 1 injury was just inclusion so so the schemes so these maps each of the next the air so I had to the kingdom Meridian is left to 1 right and into the accident you can you can use them on variable remaining in this land the case and that mapping to to the experiences of so so so these shows that these factors he's in the will we would like to also say that the other factories in the orientation of the University of Miami have so so this map if you want to sort you count these these efforts over the years and we have some kind of capping here you count them by counting their their home much a wraparound then began over generator all of these guys just as sometimes auction and and they ought to order 2 feels that the variable so that the map does not see if these these days is that the accused appear lamented someone just inches apology from Torres to the solid Torres is identity United States XIX and Peterson and that's what this map does as well right so see if that means that the fight if I could it's the peak was 1 and I define my chain map like these I have a change so therefore it is the peak was 1 easing the augmentation the writing and these factors it's an opponent of it's so we'd like to understand why this this thing is here and it's there for similar reasons but there is another reason other than than a feeling that the insults excellent let's try the many ways to say this but 1 way the saying is the bomb that introduces the history I haven't anyway users stream on the north rates of 2 years of history in years Arnold and I have to call normal and going out like this 1 of the boys but to see if it is then call normally intersects the there's serious the Sears section along the north tonight in there I and basically live on his looks like that then I I can now them so that they get staying in and what I do so what they desire I take it serious section I joined the call normal in the topology of what they get is actually they're not complement so I have another feeling which is slightly more complicated than goes and then spreads over as histories of that but as the topology side conservative think it is excited and so or if you if you want to say that from beginning can take a functional Moss function that sort of explosives along the north try and take the graph of the so so I have another feeling that the MTA which topologically is just as streamlined it's not the and and and that if I just care about this incident always interesting topology here but if I care about the quality is not so interesting is the SEC accused the longitude proved keeps them the so so therefore I also have these factor explained by counting the on the southern along so to this still excited audience this somehow forgive me these factors and that's the kind of proof of this it know was the 1st was just a kilometer less wrong co-owners of going down to the serious action is ongoing and the isn't so now and as you see these these words great for this Q equals 1 and remember that Cuomo was somehow he was related is that each of the charity is the class of this festive so here we feel there's too and there is very hard to recover to itself what what what now I want to explain is what what's that what's with augmentation polynomials when Jew is not equal 2 1 and how can we see geometrically there and that turns out to be related to a lot of physics so I want to kind of give just a very brief description of the statistics otherwise it's similar award just when things come from and that's a sort of war-related overview advertisements or something and then it's sense is a long story in physics but but entering the starting point for the stories His giant theory and that's what has been From from physical point of view is you 3 manifold and then have a chance I'm actions as it has called on the UN connection so 3 men of all of them and then In a minute said you inclinations and then you take it this is a section form so so this action former somehow not quite gage
invariant but it's that it's the changes it comes from some characteristic class in 4 dimensions the changes by multiples of 4 apply if you change the engage the 1 thing and then and then in 261 right down the path integral which is a function of the of the underlying manifold and diseases of Athens really sort understands the integrate overall gage secure stress of connections you take this into that I carry over for pirate Kazan integer equaled the level there all these
jurors I'm section so these objects from Asmara .period does not make sense but you can treat with Fineman perturbation theory and then get something in the end and basically if you do that you get the expansion in terms of social media the expansion and in terms of of K which is this level and and on which is the the we quit which is the the UN rights of em and then there is the starting point for a forum for election is actually Britain's all result from the have from 1992 the new law on question the last thing that you can expand it and so did the critical points of this actions financial the flat connections you can kind of expanded around this that connections in some kind find expansion and I'm not going this this and this and that where a lot of these none of us have been with and so much so that we can In United so so that these these giant Siemens essentially related to 2 topological string theory which is of no 1 in our liberties and run with the so so so what he says is that this giant Siemens there Simons partition function is equal to a certain account so it's really like coming from topological sincere about when it localizes
isn't is a growing with invariant and it's a it's a little bit strange going with the new
variant from our point of view but accountable Norfolk cars in the content is fond of calling on em all em with boundary on this hero section but but you have to take after take and corporate so-so scenario you imagine it's like this we want this section but not the drug in the top waiters and you never exactly and copies of original lying on on top of each other and the such behavior too so that we can of it would be strained coupling constants of this is the genus parameter that use when you expand just like any of so this thing is century so the basically what what we've been saying that this is supposed to count for Morphy curves in the store and with boundary and now being generally well-educated simply Junger's say that there are only constant such such maps but if you look at formerly the dimension to see that this is a three-dimensional Calabi-Yau manifold and that the serious action as mastering 0 so formally any such this is regions there should be a count and and and he invented something called string field theory to related directly to the trend Siemens cancer but I think and this is what made him great take that "quotation mark project to make sense of this kind but that and the he wanted Reuters which can but the level of the during silence "quotation mark you and you want to know write to them should not be released during questioning it was considering them I always thinking of ways in the No no no the nor the of sources say this of right 1 of those who is the the son of specialization and some idea how which From the status of the functions 1 when was the last because you want to compute somehow the volume of this space for the villages in there and now that I don't know outside didn't think about it much in this industry but in terms of the kind of coefficients and the expansion was coefficient of summer means something if you go back it's in on that side yes but maybe perhaps not on the side this no I don't have good answers I need to think that this was a kind of normalization of this water is weak amounts as you're saying this is not quite often but no major because we have known all but it will become it will become and the normalized has allowed what is that your assignments at the coefficients it comes and goes in his house the light of expectation and the all of which you and the actions consequently the position and sold his soul to the response the the user and the way I the modern art and while I was in the new life statement should use words the 1 so let me can only go 1 step further and perhaps can perhaps this will answer your questions so so then the next step in this story is somehow but worry about and they want to somehow then there so they they was qualities Konefal transition as a way to relate various was this during a series opened opened and closed string theories of it's also not understood there was a well-understood mathematically but there is a physical proof of this strange correspondence so here this is a picture of the star is the showcase forestry we then copies of the 0 sections then then In the stories through you can view as the quandary King C-4 and and Europeans being shipped through through a cold where 0 section but now I can resolve it the other way so
instead of like this in the case of a feeling that through blighted these publicly instead I can feeling the S 3 widely published so what they get topologically is someone just as two-time saw 4 but it appears nicely for years centre-right John tree languages that the all miners 1 London received the 1 no what I want what vis-a-vis predictions sensitive Fifa's experiment that if I do that all but this will weaken over here that is related to clause the serial killers cars here so that Singapore and so on I have to require some relation between the areas here and that that there so I take the area what is it you want domestic indicator parameter of his manifold is the best finite and that Singleton coming caused industry incoming calls at times and so I'm sort of letting and go to infinity and he's going to cereal in a controlled way so that it ends up at the and then the all but Roma Whitman theory in this case Torres 3 cleared chemical procurement as 3 should be equal to the closed growing reconfiguring the kind of role with encounter in its school expertise with this identification problems so there is yours I think you is that the the so now the easiest thing in the right hand side from all head the that I think you have to some over 1 and so it's not a scientist said specialized daily through only Van Gogh sentences against the yen but there is no limit to how many can recover this case he was some understand women here because he has ideas and the service OK so what can we say so somehow these can't count can be done so as opposed to the delicate count cars here in the area conducted and on the Panamerican militant and and and that these and I am sorry I don't ask you probably can also it's expressed stern Siemens and they are in fact amended some Atlantis's check that they actually agreement so so although there is no mathematical proof of of the mechanism in these cases mathematical check of the prediction of these things so I did what I was going to be with you no knowing that these from weak and I think we cannot quite the what we can we can expand and that I am sorry to say exactly as they couldn't answer your question but there is a way to write that somebody else probably knows well to write this petition function forestry and some rather understandable manner and then there are the answers chicken so this week that's what I didn't makes the singletons disapproval fact and attractive to fall with them it said that there was what I suggest maybe can From Here recover what to with because this is of her of more familiar than what I would like to hear from you 4 of the physics explanation of what actually goes on with the space you want me make it this and I'm not going to be people but the incident was so focused also we receive we want to include not in this story and methods include not used you just have to work safely and why is he here and that's exactly the call to win their release this year of the new basically in world and involved basically here you don't care about smokers kick some butt so so there is a way to include not in this story and this is due to I said this is probably not aware of what they said is global ,comma laugh about it a rougher and so it goes in eastern also in order to include not I don't know so what we know was we take this the strained and remember this is necessary so that that's the end copies of missing out on its own then we added we the call normal the goal normal and now we won't account of Moffat cars in the same spirit to win several boundary when wind we they can look what they really want but there's just 1 copy of al-Qaeda medical busier and then and and and that can be shown on the trans homicide to correspond to the insertion of the something in the path integral and basically what happens is that you know as opposed to take this 1 -minus he connects with the utilization the theory which rich so they is as long times or again and his x basically corresponds in the 2 you 1 connection so it's a lottery around these generated from OK times staff only 12 hour connection a prolonged case this is a this is supposed to determined and so there is some value is the same type of argument as we can use from beginning somewhat continued but want this then it comes down to and cost now this is why I don't answer your question primarily because then thing that's very interesting now would out drywall blizzard they speak expectation values so too is the most enormous for K so here also and it is but anyway so we normalizing these my history partition function so so so it all comes out in fact here he's like other home the polynomial so you expand this has the talent and any gets is a symmetric the traces in Sumatra groups intentions so soon after all this is just the start although all the gave the home to palaeontologist symmetric there have been put in each of his communication into congratulations but anyway so what is this is something fairly possible to calculate a polynomial there is no polynomial when you just used his S U 2 which is derived from some chicken computed from foreign by some relation with coefficients like these the polynomial for this guy ,comma for that guy of for the it's 0 and some coefficients and some of iteratively and the common on the it's not quite computer from that but you need to
take was a cable but it's fairly fairly computable saying so the smell what we see as we really see this this picture and what we would like to those who would like to apply there will become more often outreach to adjust to a goal from the from the from the cold and my lowest returned to the result Konefal is and we can certainly do and and believing in the 1st strange statement and it is clear why as much is widely to really want to do it because this is this somewhere where it's possible to count so that's what I'm what I'm aiming for so this is kind of a quite nice manifold like to have its is a complex is not a call by plentiful but it has a chemical by and positive infinity so want to have somewhere to kind of make it made sense of such such things like his program is not to grant such camps the right to vote it was all I this so far the site some of the give discount we understand I think discount we don't really understand as well so but what would happen summary 2nd associates provided that necessary assume for a moment of the call normal does not intersect history in fact you can always use it often lead to the many of skipped the explanation of that for now and and then imagine that we have these cars because of his home cars which used to look like the they and on the obviously 0 section so now they in the transition what I should imagine is that all the halls of these cars they can adjust shrink to 2 points and then it's clear this is in the store history and if we believe this is clear what's going happen in excellent acts these just stays Simone did get somehow the schemes that so basically what all these things but this is the chair telling us is that these functions should be equal to the global with invariants of NJ eggs divided by wall close personal so so-and-so so so their homes polynomials encodes the Baltimore occurrence with boundary 1 the city its content the hard work and no no more poor condition it is just for illustration purposes evaluation development in street kids is not anymore .period effect said In the physics professor all sitting there sometime this summer of but With these Mississippi just now that the In order to distilling capsule 2 was keeping a little bit of the communications so announcing saying toward so so so let's call this function the perception of the wave function 12 and then 1 can 2 we cannot tried to play down the contributions from them as 1 of the seats in the during as the country was asking for the borrowing to the tune G 1 the the 1 John Simon's own on this as 1 times auto and when you write down the there the form the action you see that what you're going to hear that anything that is in some sort of forests in the connection has scant period P and X and water during it's just not the right of the patent medicine that you just doing quantum mechanics and service units so the times of the actions of our periods being so therefore what you find when you quantized is that you should replace some of it if you do so you want to that was a deep geologic or you won't hear 1 chance I'm series on so that and and I said I was supposed to as opposed to counter the watercolors the vote will analysts you just once also going to try to count cars from starting on and then again closing up but that we really small cars that just kind of constants in some sense the go from Al-Qaeda itself and I want to insult says get rid of them and I play with is gaining reversed because I know by weakness on whether they would be churned Siemens theory here and in words what happens is that the chance Siemens theory all this just looks like a bad thing that looks like quantum mechanics in variables XMP and and then we know what is Qantas from some kind of animal with a high school and and so is the 5th so so so that means that we should replace P minus 2 years the subpoenaed acting so that's the began multiplying when it's shortages strings P acting on the right way Fleischer should be the planned to use the system of but in this sort of thing them and then and then it was a remembering next year's well concerts services to remember that you can them express the the wave functions In this godless shortwave access decided arrived when when you have this have Jacoby theory identical gives quantum mechanics of so so so this is the sum of this suspended expansion and then becomes higher higher water kind of zeros GST is square all but remember what these losses this was just is still up there was just accountable calves and energy as well as the genius parameters of this is this is here by our other interpretations supposed to be just that these potential source of quality W K all states so this is this potential the don't To accounting regional rewarded disks Landis's forget about all of all things own topology unit and just counties so this thing is predicting that it will have P is the W. K the and in fact looking at the whole thing is what the quantized saying the homes polynomial or it's recursion relations what you what you find is that these should I haven't really saying very briefly what what's what happens but then ratio me a local parameterization all as calves and in other words so what
what so-and-so if that's given by a polynomial right polynomial the aides but many other anyway right came into the access to the pedia keeping the Stuart I think of it possesses a variable so this is another of the even and so that basically you can compute a from from the home 3 colored home the were a piece of it and then what was observed Landis's starting point for this fall clearly and its joint work by myself and many and United can offer so so what was absurd was these 88 it is equal to woman patient polynomial In all isn't so so I'm going to try to explain I know why that is the case socialism and line at schools so so so now we can sometimes forget about all of this physics background levels stated so what they're going to try to relate is now we don't try to relate the indentations With June nautical oneself more global things please accounts the so you just go in and on the future of the world you want to know and love right if you have many components you so that you have the wrong given by actually many aggression is still at large England in the in the space and the basically this part of the story is more or less the same eat it will again give various branches of this augmentation variety but again and again that the good that these then there is associated so what sorts of basically if if you have many components link you could also have another connected feelings of those components for itself she cannot just look at the coal Mormons but there has to be other McGraw engines which allow you to maps mixed courts supports going from 1 to another down to to something nontrivial as well but basically all this that they give a variety which should be the characteristic right fielder the margin of the whole thing again so that we may be out of reach that point to that as well but that in England have medical policy it's a high-dimensional variety that addresses the status this is what I the the did he the Banek sector yes yes yes yes and that and that if I kind of England fast enough to get there I would want to explain what that looks like from the point of contact among these is a more complex liken as if the version is called the demolish should know this conversationalist look at so it's a little let me let me look at what we have so we have missed it's In the inside 6 seats allocated according to explain how to choose a daughter 0 sexual abuse and I'm just going that it had so so Herndon and we have his name is located inside the area recount of which I recall W sub K of acts and this accounts for all of these films were watering these and then renders colonial cities where warranted with on and on and on empty know the thing that resenting Uncle Frank so it was a searing calls but it is inferior so this is this so 1 can question how much of this is really a prison terms of admissions here selected among local Internet discussions and quality of the anyway so the number of the various that if you take this page is equal to the WTO X it is a branch Of the inflation inflationary the decision the U.S. on their right to maybe I should like to it's apparent only need to two-year Woodward promises some count count currency in that Gretzky dance around it is the reason the there's a brand as locally branch of the International is the only player to find I would say so yes and maybe somebody else Qantas is maybe maybe maybe not in this hour only only hint at how it would be defined as the width of the cake made by the it's borderline defined if you could look at the foot of the hill but noted this was like the is supposed to counter His opened Norwegian invariants so is something of framing contribution as wearing of any this is that definitely you need all this can have strict regulation machinery of so I can get lonely Is it informed him the but with the click a head cooking but note that what is defined as a defined annulled the augmentation varieties can very rigorously differences on transporting some things the Infinity radio can actually dimmer them perhaps look what this Gerald is his audience so we're keeping track of the full of others these this has as it wraps around here on the boundary but also there is that city 1 there still inside the souls of those moments sorry is acute it was a on condition that 1 of the things that you inside and the life I'm gonna explain it in so a candidate heats up to now let's let's 1st rise of felony go about proving something like this where we were just trying get on with our old scheme we will try to counter off occurs like these to define they find the augmentations again of region's things these people here like that and try to prove the chain map equations we have to look at one-dimensional model experts but no 1 is again huge difference between this the previous thing and that's that's what can happen is that some kind of boundary bubble source forming and and then users of the relative the
version what works what the museum this all this is values case and the whole the in X and now I have a it's a one-dimensional model basis of some of following these alone this is also an exit boundary OK this is next them so what I'm trying to explain is that there could be 1 branch a family that splits in 2 really this problem sorry it a one-dimensional these from above pandering east form the man gesturing so this is a the abstractions of the deserves of that that would say that our previous nice thing said that this change fight composed today is 0 that's not true anymore so it's recanted this is the about the case is not accepted as exactly and that even the manifold of quite excitement but but in particular could be they'll start in this year and unlike and was later this is called a mention 1 phenomena so it really matters but now we somehow learn from we have to overcome these things so that's what they do moments talking about you have to find his bounding coaching chains and yeah but was the snowbound in coaching because what 1 would like to do so yeah everything is regions and on the it's not so much a modular spaces have to care about but what what what this game is that you would take these days there is this idea tried to find is reduced in trying to find a chain bound abounded that is about rebounds insiders want and saw the will course you cannot because as long as this 1 has a duty but you can go with 1 was the same thing you can pull out it's homology to infinity so we instead of finding bounding culture refined sort of the water quality of the mistake for each such so for free trade in these now sitting inside its when boundary of OK and we take change puts at infinity looks like some this is so this is a change in inside came so the boundaries and as 1 is a circle sitting inside OK and we think abounding culture in the running channel the coaching bounding chain which begins on this guy and ends on Cape Times takes some kind of at infinity we have Nice longer-term thing and then at infinity business cycle just looks like it's administrator of the multiple whatever multiple is that is required by these X X is there a low-margin was so maybe I should call it Siazon incentives specific and now huh How does this Duenas problem when it cures it in the way that land when you when you you can also perhaps this thing by counting is that these like we the assertions of all the bounding color of the bombing chains so so so when when you these these areas are organized as you go into the boundaries spitting and then you have these bonding coaching and you continue then there the you continue the family so this is somehow this whole idea of the maybe not all of the businesses would be fulfilling this is for parent instilled in this way you can now the avoided these interior speeding by at the cost of upgrading your these 2 accounting not just these these days people sureties but but you need to count rather these these so I sort of what is beautiful pictures and destroying his schematically lines that and sold by counting the we the insertions these things right so no what would the compactness theorem being so we took out the bad part of the boundary when the compactness theorem no would be that we have no interior space there so we have speed things only on the following sort this is 1 and it's 0 but what course we need to keep track of all the insertions and there is no guarantee the diary insertions leave only in the Compaq Porter they could certainly travel out To infinity but at infinity they're very easily counted so if I have 1 of these beasts which nowadays in the differential and now that the infinity my changes just looks exactly like these words so if I want to see how many times that these these culminating insertions can I do I just have to keep track of how many times does it intersect standard currently and if you think about it so at infinity the the chains that come from these guys need really looks now like it really is a looks like these will vary because the KMT to the carrots pure right just copies of this thing 1 for each these so you had this to say another word counting these assertions is the same thing because if I eradicate times around I in Angola once European Union started caters to exactly set the fee is equal to the wkt so if he if I want to counter violence have just 1 per year it looks like the decay its and now I want and I have another car up here which goes with the fight after close of those along these these a circle so how many how many Kirsten account when I can insert this guy I could use 1 of the gay points right but I have K choices for so my counsel times to the case and therefore you know I have a few Republican officials and some of the mechanism exactly the same so if I put in penny equal to the W then these upper guy in the differential counts cars with these assertions and the fact that not is this matches there is the proof of this thing that's because From the means picture prose is clearly defined ordered such as that in the days the China progression homes then there and it's it's you know making this substitution it's exactly the what we should do what we we came here he said to across the different kinds part of that will for example in the 1 and only example that we know you can now count if you know this can live on General Donald you can count count concentrate so to knows about this this is 1 of only Arkansas so for being in terms of next and then integrate once and you find this potential for this London inside so so did so by knowing the augmentation polynomial Michigan computer by elimination series so for the dreadful it's more complicated thing you can now count on awarding these rebounding on this London inside the 6 Q With the Jew captain yeah so it doesn't play a role I mean it just keeps track of how many times the traps along the the central city once it doesn't it doesn't interfere with the boundary here so it's just carried along it's like you some said that don't dominated this was W and then the W the thing that you want that's just curious just just Casey Khaled the excuse to it's just journal this would be the French
nontraditional you know it's not but if you think that it was as it is it's not the way but they wouldn't have the right to the heart of last last of which is what is so here you can use those these these would be like calculating their equals 0 right then you know that you're supposed to take this but there are many questions using particularly in order to recover the whole when it's irreducible you'll find activity and that sometimes happens but not always when is not just a moment like find morally Johnson too 2 4 to cover all of the consultants and I don't know how to do that so I realize I have no more time but let me just maybe can say forwards only this for discussion so so In the thus as you know I was saying so that there is this supposed to be the least of these things always so that that upgrade so we have this ornamentation going on that upgrades this to an operator relations with the same symbols but where where indeed this P P now is equal to GS EDS in line with what I drove for the wave function and and this is what what happens here this thing should kill them this this generated ideal corresponding to this trend integration and of the risk of the model and then what what we're working on it very much a work in progress is to actually see how to use as of the so too the counterpart of this contract to Montague but instead the use it's also 1 the appeared and count and and recover this these relations so so that's and then manage somehow creates an interesting story I think is far from finished but that it's looking good so we could well on not somehow cheating but managed to therefore hoped Lincoln for transforming it looks at him interesting it certainly is that has a lot of challenging almost recurrent problems were among them and also is the author of this was structure London growing and also I would say some new phenomena where are you recall scandal multiple times and so on so maybe about but I think I'm going to leave this to the discussion the stoppages was in the home of his Will you the he and on which the also yes that's that's the percentages and the properties of the stricken appliances this was fairly generally going now here's a very good case when all the colors of already but if you want to go into applying this year you could you say that when when the homology whenever it is like London's with some infinity and knowledge of the London generated from Infinity then you can always pull out cycles and is the kind of good as monocultures coaches and then you get the maritime regulations if in the non-executives but what about the cycles that inside shortly and amount water they are behaving exactly like in this standard competent wander from origin story but some of them you can get rid of my life transporting for infinity and and what is the lesson worries that this is a it's actually kind of quite efficient way of computing I'm so sorry and I would say that the contractor was also did this orientation polynomial marriages this 1 is a it be difficult but this guy is just that as I said it's just countered by by by elimination series from of something very concrete so so so this calculation is comparatively very simple where is this other computing directly inside is a kind of difficult task at once it is mentioned in we have to but saw the Council of course on drawing pictures of his going during the opposite of the strips of Florida voters in state of pejorative as head with the theft of state what so the question is really what this this is Norwegian potential so remember what what presupposes a restart from something and we realize we have to count to disputes like that so we will have to count you know it's insertions of this bounding coaching for this guy here but no but of course they they could be some sleeping with some of splits you cannot say when things :colon so was a when you think about this it could be that some of the insertions or some other guy actually ends up here so so that the the count all when what they there these potential which I'm saying just companies that's not quite just count beasts oppose the work would be falling because it will have to count these read these binding coaching so so if I have 1 and then I have already can of some lower energy bills I have to count that these people want 1 possible trades on insertions all other these uncensored so so actually there they these go with count is depends on that somehow the choice of his cultures and as an intimate like this refrain the boundaries in some different way you get some different countering so that's a hasn't and bonding the framing of the utility or you can maybe me look borrowed the framing from Framingham on the Soviet or something but admittedly I mean this is of the CIA the work out in the details in hands of of indeed this level but I can they have you just just have to it was you know that there there are a couple of different framing so so that 1 1 framing that they talk about is the largest a choice of bases X compared to P and cement and basically these these guys should know everything can make it to the change of variables in computing but realizing it game is somehow that the prefers a hears about it my feeling here accuse the period if you do something and some other from before we would like to kill the variables that just sold for in this potential for an a priori don't don't know how to get 1 suitable advantage from them but basically this phone owners should know everything the best thing is that that's the think but then to create the geometric something for which it has a very all of you by himself on his so we may be in this that is not this is exactly so if it sold by during the year but thinking about the wall the kind of hygienist cars that you could be by insertion as well To save if you for example if you have is the east and you want to insert these guys and these be cities but now into hiding as you have to connection to insertions you can choose balls and so on and you find that the account just exactly what you get by taking the new thing when the American explaining discussion so there's a kind of worker accounts the missionaries In the at
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Metadaten

Formale Metadaten

Titel 3/3 Knot contact homology, Chern-Simons theory, and topological string
Serientitel 2015 Summer School on Moduli Problems in Symplectic Geometry
Anzahl der Teile 36
Autor Ekholm, Tobias
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/16320
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2015
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract We explain how knot contact homology is related to the physical theories mentioned in the title. We report on recent progress developing symplectic field theory beyond genus 0 and how this relates to topological strings and open Gromov-Witten invariants.

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