A symplectic invariant for contact manifolds
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Title 
A symplectic invariant for contact manifolds

Title of Series  
Number of Parts 
36

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2015

Language 
English

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Subject Area  
Abstract 
The construction of S^1equivariant symplectic homology with Alexandru Oancea can be used to define an invariant for a wide class of contact manifolds. This is a substitute for cylindrical contact homology, which often has transversality issues. This symplectic invariant can then be applied to the study of closed Reeb orbits.

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02:14
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and Hey a and you can I'm a thank you for the invitation to the interests of the next summer school it's a pity that I couldn't enjoy a little more than an hour to days of this thing but he said nicely organized and we have the feeling that among the kitchen and the this that's what I'm going to talk about the dangers of some joint work with expansion and so indeed so sodium the idea is to work with ghetto invariant for contact manifolds and if she would I would think before Mexico's win Over the most natural thing that you would like Europe to do with the issue a contact any forward in the Pacific the manifold is so it's certainly something like a contact homology and what I would have to I started discussing it in the Senate resolution of this and that and which is the same legal version of contact and so I assume that you many foods company for Whiteside and on knows the dimension of the contact many for barrier .period minus 1 and as we usually do In this series assume the contact structure to coordinated so that it is expressed as a of 1 form and so reduce showed that this 1 so none degenerates you can achieve a small perturbation Italy's means that issue I the cruelest Waibel that is on the point that lies
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so that's the way it through what fantasy for somebody to get
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back to work to be there the issue gets the differential Of this week for what time the restricted to the contacts hyperbole .period than this House
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no I don't value equal to 1 and the whenever you such situations modulo some choices of today's edition of the Compaq structure along the trajectory of starting and ending at the then you can associate justice and orbits of the Canadian excellent valued index for such such faults so that's 1 of the ingredients the choice of women degenerate conduct forms that is necessary to set up this series and the 2nd ingredients list at the level of the same victimization of all contact many forms so the use of the products of wine with the realize equipped with disinfected formed the core of the I thought with the quarterly the wrong this is realizing that specific decisions and on Saigon shows J media compatibility most complex where the Ferrari properties the 1st properties that GE preserves the contacts distribution and on its another demeaning of the received is compatible with the syntactic structure the it seconds at maps the vertical directions you overdid the along the the line to the way Finland while contract for and finally J is invariant when the translation so these are the 2 ingredients and who whom you need to set up this ,comma logical theory and once you've made the 3rd destroys you can consider now modernday spaces and on and moved by an Indianapolis Indiana minors the model space apology extended John the program warns you you are defined in the new values in part thanks wise areas of the heights of function and you will be conducted in the context many forwards are so just knew that the editions of this intertwines the world so complex that you understand review most complex virtual on awesome Brickeys Asian and with the following Isadore your properties responding to this day that he and the definition of space service that meeting the for the it's going to press minus initiating so he s stands for the court in the line direction on the cylinder of of S and was the top of the anger quoting from a single digits reminds affinity and delete fastpaced Boston personal minus infinity of you and what is the impact is going to be given by you it's Gemma Pressel miners in the 92 To put some more but some factor here are some of the universe and it's ridiculous so just sticking to quantify that this this is the of this period 1 on circle by a choice by convention and always of course can have different different periods for the week and so this is a modernday space in the sense that our accounting away we are putting together solutions of the PG E with these asymptotic you're around conditions the module module Bahar Moffat without much resistance Of all cylinders and the translation In adoration In the end the targets since Jason Robinson his direction if you have a solution in the 52 year European solution so that some of the modest spaces adolescence was a world tour event etymology of the cynical version and you're no if there is a trend that started the whole for the elements of this model is based in the northern dimension of his abilities will be given by the final index of attitude problem and examination given made a difference for the going entering series of yes adults minus 1 and minus 1 coming from the caution by opposition in 1 of OK
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knowledge me but the decides this important restrictions or combat to it in a minute and it's a continuing leader with a construction now that we have this analytical ingredients begin construct white objects in your chin complex sold defining the contacts complex will it's cynical incarnations start stand for grading of the things and this will be a lot of the presumably generated by on the 1 most rewarded for the good news is that what every the for the twowheeled refutes the existence the shortest trajectory that seen image Oregon compute degrees in the index for the the trajectory and it's a seabird counterparts and his goods if and only if the parties of economies in the industry .period went to the fury nearcollision refusing to check conditions on the video recordings of Nordic and this is great by not exactly the going is entering data shifted by constant and minus 3 remember and the dimension of contact manifold and the reason for this shift will become apparent in a minute that conditions will be spelled out in that more natural to express once the shift like this now this is so stupid interview 2 jobs for your purposes so it's so sometimes would twist reduces costs more objects that's really something we typically do .period bitch it but if we want to be classified loans the wife and I can restrict myself to the Bulls Waibel be that are in the class and it's something already potentially smaller depending on the quality of so that's just incorporating the way dynamics and now for the good of the whole interest when you can find the suspension of the sooner by the findings of some always rights again after analogy with the addition of my motorists face to the sun Over although orbits and in the world gamma minus would leave the property that the greening of gamma minus is wireless then the weighting of the you can't elements newmont space which it is not really the the ,comma filaments in 2nd Amendment rights document associate assigned to work elements in 1 respect virus from coherently rendition
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construction that I was getting into to that for you golf assigns the elements of his mother space and you will vie with questioning and bottom generated and when you see the fact that it was because several field of it that is not an issue because definitive gamma minus appears in the defense of Kannapolis than they are homophobic because of his mentally gets into different here and so I the hope is that you can get a home mortgages series a display on this thing will be presentable but the study of the generation of formal because shows that did not always the case of the CIA's Square is not always going to be the work was and that articles of cylinders in a muddy space 5 business model is based on mentioned 1 4 again under presented assumptions but can also degenerates this will not only 5 Google circuit centers which will be counted by the square of the offensive but it can also degenerates into another configurations which corresponds to a bill bans and why polymorphic billionaire and yet this is a vertical cylinders or will prove to people because of this configuration listened to 2 separate copies of authors they this piece and that these refugees index 1 I saw on the issue during the so optimization business the index would equal to what once refused to tender indicative of minors economies in regions of the world I was elated degrading the reading of minus the sum of the reading about the he had agreed in a telephone bidder dimensions and of course this in these isolated incidents and excel in Dixie has so you that happens and then efficiently the is where counts this innovations into battle scene interest which is not equal to 0 equal to the god of these objects and so if you want to get a differential and we need to prevent that sort of phenomenon from happening In 1 way of preventing this phenomenon from happening is to prevent this albeit with radio collars from existing mind if I called these orbits Jemma up then clearly due to the fact that the index of these elements here is 1 the morning reading of United that is equal to 1 and of course since the plane is a convertible so His means that if are under at these ideas presented conditions we have the flooring reserved for this construction so if can from holds and Minnesota imminent and he she was curious enough to avoid such phenomena and this means that you ask them to conduct complex evil we will notably glass profanities when winning sequence ones 0 0 minus 1 then this year's square to see what was it all and the sitting together on technology In Class a which is defined as the of the complex invariant 12th or initial contact Mitchell so here this condition that the complex trivial in reading 1 corresponds precisely Newfoundland hits as to guarantee that's DEC square between the museum also you can define homology and the storm conditions are necessary to show that this mortgages in OK so that's how you have a nice tool to study a contact many Forza but the mitigation Is this assumption because of it is very very Waleed satisfied and so went that cannot sustain exactly you under which conditions is satisfied with the hour at 2nd show was situation With is I think you want situation like weakening Meeker statement and finding many words wary when show the swords and you see that for restrictive sold 170 warily holes and is for example the case it 1st 1 of
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them note contractor closed we bullets at all of the men and of winning so this means that simply connected many canapes you can work with and 2nd you need to chill the glass if we were to be because agreed with the closest to construct a complex so that it contains finally symbol Close to evil the rejected In the connection we have a duty to read it and I think that I can win hold might fit into that sold you need both conditions be satisfied and that's an example where it does holds but that are going to give you the genetic conditions more than that in these for which holds meetings on the specific cases using some adult argument depending on which they speak the sequential can look at something that's the way that that's that's more Azerbaijanis begins candle so that's indeed extremely restrictive and and reason it works is that the well if fell you share of of these 2 conditions you never of course after World War II about this kind of situation independently of presented because you don't have blades of 1 and the 2nd on the cylinders you are going to work with since you are the essentials will inject a sudden jolt begins so that the laudable exhibitors will also be fourhour invective the of DG ends and by your result before dragnet then it is sufficient to the meeting to choose you almost complete Fletcher as both in a generic way so that from Saturday and so that's missing is the 1 who 1 case where you can do something with invariant but it leaves out a lot of where the French with Institute found that almost all of the all and that of the should take care of the unit wouldn't inventor of some hyperbolic manifold I don't know how delightful coincided geodesic fluent in uh than you can choose a Sensenbrenner homotopy class so that is willing to work with Adebayor jitters again you don't have compared the 26 were so that's 1 we can do as a foe of many forced you can find a few orders on festivals as well which will come on top us did as well but well that but many of the countries that working so there was of handling but I the Class that if we want to be classed image so you need to be decided to restrict also contains only simple poultry be I so that that's that's cheap you can always choose discussing this but of course the the difficulty that maybe this small piece of the United but whatever you want to do it right but the total was used now OK so um so that's quite frustrating that we can to make things were with 44 series of this area and that many of the policy are interviewing them mentioned free of disease of high quality called this is the bad news of OK so let's see what else we could do we could do In order to salvage the situation and still have something that is pretty similar to the south this construction but that really in much greater generality them the use of very heavy restrictions and when we do that is to adopt some suspected point of view and worked with this 1 in preventing simply what is the big difference between American that origins in that equality that now we have been looking for a series and 1st units next what ingredients which is to an infant so let's consider 1st new mode of 100 union functions more engaged he finds bomb or simplistic many forced nudity that Asian of wise well 1 and assuming that the user the stage behave as in the following a schematic picture I'm going to the wall a sketch of the graft of of it as a function it will depend only on the cheek coordinates here and instead of writing the ouster of edible eyewear development the exponential and so this means that it takes value from 0 to 1 to infinity and this morning it every year we'd give it some of asymptotic you're conditions asked for that very large volumes of Bamako distinction has a flying Weeks floorsweeping is something of a form that dirty dancing the duty of the gapless resources and constantly that whatever it and
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on the other hand near the original adds that it's that even a very small so please so serenely out there with the and then we can determine who just point In the case of the jitters you give me a candidate with with Redford method OK so um now if you choose having to information well the rest would at what not having joined in the effect of and associated Industries is doing because that's how we need them the many of all its 1st series and so it is hard to know that a few years entering going to be minor the United from distant from engaged with respect to what not to do this In other words they believed that the multiplied with 2 which went so that's that's what you really find out and so this means that the blonde Of the having done and that BakerFinch I am dictation correspondence with clause to waive all but with the constraints that the periods of assaulted did not take values set out in the this is that which is between something very small so we can assume that there was no period of growth we will bits of betraying the slogan is important in the scope of its forward and cancel the cost we will meet with idiots In the and in order to avoid the unpleasantness is how we assume that this financial capital chosen generically so that these notes the for the week definitely you will need not have Gross orbits in this region all but the illegal which would actually be contained in combat region of your OK so that's so that's a very nice having gone and need to understand that you cannot quite well with such 101 in the world world standard drove through a series we coast this effect of fees is independent of time and therefore if she worked with a bomber tries to want will be itself is that too few of them as soon as you have long you have a whole family of it because all of them because you can you can about it right into the palm of his right and frosty we will be Spanish tricycle and so on by going to use another 120 capital each of which depends on time for a time it's wonderful news ,comma kind of closing most of the positions and destructive energy which is going to be pursued the I think that abandonment perturbation of this morning what do I mean by Studebaker but I would like to understand in fact the correspondence and continue to be able to understand the correspondence between 1 billion equal weights of not into another 2 feet and we it's what happens is that in order to prepare what you would typically need to do is to work used is fate of dependence begin viewed it as a as a function of the circuit and along the beach "quotation mark will you are going to introduce but but to Beijing in May of a function on a certain issue chooses to view the most sanctions then each critical point of the most function will give rise to world 1 billion people we of the patrol .period infield and so in order to avoid having zillions of but it would victories after the perturbation you are going to chose the minimum number of critical points for things most infamous opening to so that the student were provisions chosen so that 1 billion people rates also all timedependent have endured a bitter feud for capital each they are actually given by a pair of all beats within the move demarche shaken at for each rules we will always Indiana with idiots this means warned but before that we are going to be the new it's interesting guys to generator pulled its tool forward birth but the ball crossed we will be that he hasn't been to contact look it's so now that he has introduced deserve extra ingredients that then the 10 major but if nation for grated invariant now if we were simply doing on 1st hearing you need to work the synthetic complex which is same generated by I use a billion each audits of the timedependent coming to England this is again going to be greeted by your colleagues in the index and for consistency the previous definition and we often disagreed my colleagues in the index pressed the same shift and managed before the further to from the usual conventions in literature that meant for circuit equality here pristine beaches to make it look like the contacts of the contact that and I OK so that can be done the complex with useful old enough for a but
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that's not what we are going the other willing to do so this 1 a that version of that in Seoul seconds later released we find this 1 a covariant version of that the home of the 1st complex Italy's doing to be based on differences in Wajir which is obtained by taking we use where construction material using modular then searched water questions the disease with the polynomial no 1 variable you which has nobody to equal suspected of involvement in the Phoenicians despondent and brother no no no breakdown of forgotten that when I say generated by 1 periodic orbits of the things these includes gonna checks and the other half will possibly get the all the idea is that he has shared checking the Icahn will wind down Switzerland this 1 lesson in how to think in a ruling of the Knicks on more what in the industry fell by 1 is the most index the problems of right of admirably to use the chicken hearts In addition anymore because I don't need to this and that you may refer to this amendment has been 1 of the problems the disorder due to use of the variable in the argument from years I didn't yes his hour of course so your to work completely Gubicza with Weaver but you to do so need that's it's a choice at some point we need to remove the choice later in the construction at this point is depends on many things intervention geometries of Honduran and sorry at the end of the construction that's what we and the beginning of time and then on this the model anything you find something that will of on the Financial Times will continue despite the this 1 and all of this and this 1 will I need to see where it goes on each of the use of factors here and there you can decompose system 4 key performs able to infinity the index k corresponds to the effects on the body during that because if you over above you by the case now issue either .period known there was the Willesdon gave the sector the going you so it means that even noticed some station at issue Ottoman even element in here you only have ministers contributing mightily built convergence issue just for 1 of the on and if we reunion and they're finding jobs ends then on this factor you acts by some maps and I read the news for now does not justify case and that we need more time to define what is this idea because you the counting solutions of some moderate right so let's do this form of the origins of land because of baby by this initial contention that the effect of this lowering the we you vacate has the effects on putting of the and careful getting the right principal starts slowly and for those Ronald quite familiar refers to rewritten say what Faisal is going to work to counter to place your viewing columns solutions for the 1st equations consumers on their merits you do that not I don't need to distinguish between them I kind of went away factors involved the final decision to have the values no simply could not afford said is that you do want yes press j of the duty it would fade out 9 assists and does the effect of the coming toward now I'm during an effective sheets along fourcylinder sequel equal to 0 and you to that of that can conveyed our convergence when s lost 1 Bristol minus infinity To sum 1 barely Corbett of 250 the opportunity that because it's not we all the time when was to make its nemesis to say something to him that of August but the start of the different equation now known of course that this equation is feared that abandons the new to the current Olympic fins and sold means that there is no reason that's we should give exactly same the doctor Dr. G. as we used to have in the contact situation where we have long almost complete structure we can have this 1 family almost complete federally insured his jacket with the that event as well In some ways of the here so that's 1 indifference between the contacts construction expenditure on these constructions that now you can begin shows in the wider of choice of judging the data because it ensures you almost can't expect expected to depend on how did you get a good faith and that's actually quite important because you don't wear whatever you always are actually doing in the manifold sins but did you Dejammet the that depends on the dock always Oswald's Osinga somehow for President purposes and so this means that they are in practical situations we will be able to choose generic fear that avenging twitchy presented the force of police and that that's a big brother bitch advantage compared to the previous construction In this is not the
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index is so 0 so here so is the guys that I counted by Faisal corresponds to the fact that mattress miners Ghanaians minus 1 the was the decision convention hall it into Europe's enlarges the species of human the by your working with the wider choice you have enough To get interested for this event was crazy will now argue that it would be better if you many times to give you the differential ends up so what we hygiene we Jones not just a matter to tear down but still Tobosa there are composed of such matters those what Hamipterus pulled down by you the Boston body just stands there to say that these oral vectors and facts Wilson to while we live in this 1 To the deposed game while any buyer will in after the power game minus 1 yeah components will be to users to work pieces of data and this solutions of where getting some fruit .period equation platinum seemed out of the equation but now the difference is that both my while most complex structure and my Hammond told invective fields also the band In some ways of undivided as the real direction from the ceiling and of course I need to tell you how these more generality ingredients of the finds out of the original haven't agency regional 1 most complex procurement Jason and 1 name I'm sorry let the U.S. is the variable an easier 1 rare Israel's interests so J Of best fit constructed the former the original J. that depends only on fit a home from school budget here by sitting in the car equal to some function without In the mother and similarly this coming to an end of their that depends both on S & M out the theater dependence was implicit that was always they'll calls to bring the tall original humming Georgia but without even think that being said he could to some functions the that of a fear that is now what I have to tell you which is what is essential this decision itself this fatal followed final recipient and so police detained was dramatically Holly depends on this was my realigned its valuable OK so for no less than 0 hitting the dog the quite simply To say that the equation this a Woodward said I of overnight freight which now after 1 things are changing and they will be changing into units 1 of the 1st component of this edit In this region between the fate of minors Taiwan 1 so we basically of shifting the anger by some other anger so 1 which is the 1st informed of family and he between U.S. and military no 1 and I want this 1 religious constant region loosening the interpretation the next 1 where shifts by total and we will keep this constant value and you a 1 per cent then you haven't pollution here she therefore division 1 you begin to prison and implement this until you reach the last a special moments which is a wanderer stuff about respecting and human 1 and tho division 1 year of radiation and after that you have the final value the adopt minus style the Nasdaq stock so that's what the not I believe that is going to try to reshuffle batsmen directly about this integration regions simply wanted him this is the life of the feeling anger style and in some time at the end of the many regions of
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different sizes intercollegiate indeed before and road portions for for the which other so we are what we were curious to college triplets of solutions Soltau can take any any value just looking for so that there exists a solution you usually looking for talent for Ellis so that's near the good Tristan equation is committed as defended the greenhouses solutions and so this means that if you really look at the before index of that's and you freeze the broader Dow if you freeze starring Ellen you look at the start of this is a great and we typically for the solution that had a negative index and index victory reasoned and will back of review only because of the presence and Dow add that because you have the freedom of Redding talent and the search for solutions that will eventually find some solutions and that the guy that you're going to count in the map fighting so we Yukon cinders disinterested future that long has negatively unlike what happened before with have next 1 and because its value we Kresky a wanna was introduced into me about arose once popped out when it's tied into thinking this is going to be lowered by 1 and so that the user the continuity in US pressure index well before it used to be 1 that now this reflects the king and his reasoning that fight kid we have the greetings forgive the fight he of the winning would be the opposite of that Tokyo may have won but then you'll shifts down by 2 key Sugianto 250 I want so England on terms and therefore this differential has the effect of wind we for the reasons as it should be look at the Seoul so that the addition of this it's 1 of the differential for especially emits stranger and coming out of the office of rules and this is the Phoenicians Manitoba trysts so if I want to work saying that shows what is this year's 1 where this 1 issue on the start writing to follow strict rules of this if you need to expansion and is going to be the 1st of qualifies you know advise you always use were from the injury comes at you would think I perhaps you numerous multiplied by 0 5 1 but if I want we have no elderly sit there will be only 1 to miss between the doctor and the summed up by a single single trees and misfire when the denoted by a very dark indeed what familiar with its when it that series is the media operator and then you have what higher higher approach in a new interest the 3 command and the reason for the presence of the story .period might say OK but that's you know about this when series incorporating the media bridges should be enough some weather this eventually with officially that the school doors along not equipped was you so the presence of these services to guarantee that display of disunity OK so that's her initiation of justice when he let him feel less so now is the 1st of his 2 books about this well and results obtained during the mission expansion is that he should be assumed the news was neglected complex the CalEnergy paved the way we please not exceed 1 so that's slightly stronger than asking that bill will conduct complex was 0 when the Wii was minus 1 viewing 1 because you asked of warning it is the switch in many many kinds of examples is the freedom to restrictions so that's the Securities in isolation so if you have that then are then this is 1 of variance the Financial squares indeed 2 0 0 End that India it's 1 it could be that entomology I need to know depressed because that's the notation in meaning that there is another guy that has no present at something different in misconduct and blessed which is defined Of course they take Endocrinology of this complex so this of course removal of the defendant's fight amateurism G8 of 201 and 8 steps the it's patrolling the swarming to age that indeed this 1 into an image does depend on the attitude the 28 not removed the cabotage independence and it turns out that these collection of home warranties fits into a
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directed system with respect to this parameter team and 1 candidate directing when Deputy goes to infinity that we consider a "quotation mark will it's been in the series and the Wizard of this is going to be provided for initial contact with the Indian compared to character during the previous story is that the assumptions this is an assumption on the dynamics is satisfactory wrote more often than the very restrictive conditions of promises of here for 20 from the beginning and so we no device that can use instead of fleeing arrest the contact among 4 for this 4 4 the 1st thing you have is a ideas also reunions of you are so that I didn't matter I mean said In his attitude I don't want you Pacific Division and if I worked with this impacted many forms which ,comma Gondry then the of extremist this 1 with a person is 1 with press and somehow discourse the prosecution because the fitting and generators at Indian side defeating India on continent but you just to justify its these qualities is that if you concentrate purely and simply positions this is the age of the universe is the a word wanted for example yes you can you can do that well on the price to be of course is that so what action should ideas are contained in a compact region because of you will continue but you can also do this sort of thing and this is being done in the stand rescue about values "quotation mark then then yielded to degrees anymore because because new underneath this week the Wizard little bit of export tale complexity to think on the fact that you wanted and compatriot region etc. But then you don't have to do that in all of this band of the extent of the but this will not immediately expand quickly why this assumption is sufficient to guarantee that the Serie roots and that the ethanol will present the issue what is really the key arguments In discovery that led up purely for the 1st time since and maybe some from senators of that nature will result in more than 1 type of further great satisfying this the equation fruit that's interesting if you should look at them of In 1 diameter families to beat the West 1 looking at when you want to pull out of the square is equal to 0 where they can also degenerates instead of degenerating into global disinterest they could also generated as a bailiff bans in and the way it happens is a little bit different here because we are working with Hi into an introductory out in a compact regions of forcing the conditions but it might be that the some comedy that has moved on and on and on and against its hits the negatives and medicines and give his application and then you need to look down in on another computer that's a condition in which you recover it's a genuine James Moffett laden for fadeout or more planes for some things that you'll see that it would value of that depends on whether the we agreed and look at my soul whenever you have a picture like this than the bottom part is as bad as it used to be in the context commodities situation for transit purpose so that that means cannot hope to do anything would that however a top but is much better because you always have the destined to which here where J. engaged was depend on food and therefore there is room enough to perturb the standards she presented here why is it it so we can achieve then decided to 4 departs not necessary for the bottom but again for the top spot for now it's rejects this will be downatheel up but breaking accounts France wants is breaking up with when needed
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this all always have no choice but to have agreed strictly bigger than 1 so since the wedding is bigger than 1 then well issued against them while the the dimension of a motorist basal might now it's it's wonderful you break but after you break the top the dimension of the documentary's fears is going to be 1 the miners mistakes when they get the furniture but that's negative net and since you're from 70 then you know that adopt object cannot exist otherwise we would have a contradiction and so that's how these the Samsung is sufficient to guarantee the existence of this series because farmers and begin working and that's really the key reason for this to work for the OK so that's some that and as alternatives to realize contact allergic to it's more than that it's more than that because the coronation motivation with an expansion plans to understand the relationship between sympathetic and contacts for interview for a horrible environments and weather is walls guidance on fines and this means that he was assume strong presented some forms for contact worship if 1 side the the United States the syndicated on that emerges and of course
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decisions there was as the estradiol if the degree of fall of for list required want them in fact we do object on 1 hand the cynical a version district it's safe to work we want to be classed as a simulated version no again I can bring decision that restrict myself to
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feel model because in might from working with senators of the complex respects according to this we last were these 2 things will actually be isomorphic but Gifford they will not be isomorphic guessing wonders whether over a few so the the principle may not worry but all rational questions these 2 things are the same whenever was from false this is not often defined with lots of heavier machinery that body forward but 48 in view of this the meaning of the service here is as we enthusiastically this should be filled as a substitute for that object in all situations and citizens find wrote more generally and then all application that you have in mind that you could accomplish with the contact was the Ugandan them with a completely rigorously fullcontact many forward with that objective and that's that's so that's the idea and the demonstration of why his works only over Russian coefficients and doesn't work over the sea is the following the generator comparisons between this complicated simply to contact series and something's simpering greenandwhite apology where you have a topological space X With a certain actions and you further that the action has no fixed .period tho by the signing that there is no point in X which is fixed by the whole but then 1 results of the of of unity 1 of them into that features some point of explained that conceal Courbet nude Oh no .period affected string since beneficial so that's what I Norfolk spiteful this 1 then if you have such a space units lanterns and you want to cook up some homoerotic invariant the Apple possibilities if you want me to take into account is this when action quotient and entered into a merger of the portions but of course the subject is an expert was a manifold is not going to Germany for involvement in the case not as well as as existential homology consumer also said is the most satisfied very nice properties in Europe or new Kids this would actually installed to find the more that it's homology which in this 1 a commodity for these political space and you get something that is become better behaved and the thing is that this whole orgy of cautioned corresponds to left the synagogue emergency wide use Wunnicke that counterparts corresponds to status from breast cancer and now I'm on this side here on the left using new fuels rate a judgment on this assumption for action than the coincide overtures but not 1 of the actual USA and decisions you have a very good year hence the importance of the old news in the king had anyway and you all that we know of no generate in the scenes of understands products of office of audits and problems of you here today to raise the money wouldn't always a continent of others the moderate was to speed is 1 of Africa's but I just give you would say that I don't for these constructions I don't use it you reward structure of the Littleton additional you could do that but he I'm not doing that much of the is you ended original just over its risks example of you with them but bodies this season was going to be very interested in the business currently exists in the course of the summer what we there's also tremendous always on bridge believe that whenever they annoyed future bridges and extremely with difficult mission lasted all your interest in those cases years than than than it is defined as such rot but but in than it's not even clear indeed that this is what we was but why this other part here is fight and is invariant I thought that's an extra advantage to this version of the variance widens the position Joseph itself before the announcement of the new gets it is something really find was and still is analogous to what is this yes yes with all of them so what accession Megan's actually is a space of moves about you 20 Wilton Conn that's what it should be but that a conjecture and I she worked with them "quotation mark engine bundles or unit wouldn't and blunders then then you can but control the situation before we should look and but the Benitez's here but eventually on denied him in that this was the 1st of 2 creator .period from orbit of the interesting thing about all of them what is your hand over there were times when just want to freeze rates saying that indeed the applications and applications such as the will already known or thought of losing syndicate contact tomorrow he can indeed there and had been the book chains of I had this environment the price to pay for using the right inside instead of direct left inside is that it's more complicated to compute points of purely geographic cures and and expressing their demands that this tool to work with 5 when it's possible to work to do that and some obligations of the CIS warning that integrates ecology has been obtained the by based goods it was the Giants PG student of phonics 1 and my sense for example he shows that the creation of this invariant coincided this 1 for ordinary schools he has considerably reduced your stick before working efficiently many contact strictures and for this onedimensional of Silas and also obtained some research about the multiplicity of simple grocery on contact me for using and using the the report on this this is the country it was was the reason of it is something that I never told about anything there never was a fitting a free to simplistic point of view on a contract on purely complexities there is no final this this construction works with other things the idea of Corsican bracing practical knowledge and that's what you'll be done with a suspected many falsely convicted about which here and this explaining that he should don't have that she simply had a contact windfall provided you make a student assumptions is 1 many general precipitation the area of the services of the proceeds of the sale and that the outflows of Wozzeck again I can show you examples of many the reviews of satisfied but so will you many nice cases it is very dissatisfied laureate's immediately integrated into the world for already wise that of course many forceful gathered from many applications it in the way out of this compared to what you have the company the theft was