Moduli spaces from a topological viewpoint
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Title 
Moduli spaces from a topological viewpoint

Title of Series  
Number of Parts 
33

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License 
CC Attribution 3.0 Germany:
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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Release Date 
2006

Language 
English

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Subject Area  
Abstract 
This talk aims to explain what topology, at present, has to say about a few of the many moduli spaces that are currently under study in mathematics. The most prominent one is the moduli space Mg of all Riemann surfaces of genus g. Other examples include the GromovWitten moduli space of pseudoholomorphic curves in a symplectic background, the moduli space of graphs and Waldhausens algebraic Ktheory of spaces.

Keywords 
moduli spaces
mapping class groups
cobordism
algebraic Ktheory of spaces

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00:00
If a it is here a mild last morning talk by Professor Matson on a motorway spaces From But A logical point of view how Could more nearer warned try Get some murmur If you prefer Yes so I'm going to discuss Where a new resource from abroad if you want modernize bases And the word I'm going to talk about A man is useful He knew that the status as the bad paperless with these The mayors of combinations so that begin by recalling solid something your own Mel mean that
01:55
You know that if you get a few considers closer The closer lawyer and services and the Yukon twoweek woes if they more than this but many of them This just a 1 for each nonnegative integer a Maybe 1 of genius you have Service with few hold The as have drawn here and that sort only once they are so this all of them under this necessary evidence is just a nonnegative integers Marsalis make it it's quite different if you consider Accomplished artists On these surfaces so complex structured 1 way to find it At 1st with year assistance functions were both as these He was bigger than would show that in the end the Marsalis base has That means 60 minus 6 given by think miners Locally This an exception is tedious sequences 0 so they just them Did Context artists and the usual too severe and there's only 1 If the city uses 1 then the mother basis just a copy of on the trade so from now on you know what I'm saying He used is Baylor make would too There's a lot of airspace in G is to a sense of space from asthmatic and it started from a different viewpoint It originates as your nose in context function and the Some sense that is culminating in the in this series ends in size series So We started In and Raytheon their they consider agreements of visitors To date to And the The union not vote gave us a compact invocation of the martyr most face And that's that's Basis the company Hayden They and is The projected that But it's the Montoya formulated predictor about part of the On the eve of this marvelous faced with combat and better get ready on the sort of given that computer analysis of the marvelous based its its used small genius tool We that it understood but What I'm going to talk about it in the office space nastiness Yeah this is by no means any kind of completing a better understanding of the modulus in geometry physics 1 has started to look Curves in the back On space but you should take disinfecting manifold so that means study The remains this together Of the 4 Walter You go into into this Affected manifold And in groups 1 has started marvelous By a man and a school so that may be limited There we There are many things that come both from followed Who on the viewer from humidity from your point of view and acid sites Explaining to take up some of these themes in year in the Context into party we examined spaces for defamation so we can't bases equal if 1 can be deformed entered into the other By And seniors defamation the means who will fall the means hooligans upon is Called Of these bonds Of the space basis the beginning if we can understand the column on the basis they and we have a chance on understand space Up to if you more thought But before meeting but noted that Giving the definition of the motto Again that need them any possible definitions But what I choose 1 would particularly A good Allpurpose so that its income structures
07:07
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12:30
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19:34
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26:43
So they actually classes in the inn's will call market and by the year by the year among data justice That means Only a statement about Mexico's former My foot The next thing I would like to explain is He is The The odds These services and modernized faced with fear of and told 50 years old so the Hmong about Borders to but before I would say this about What we parted Tonche base So let's stocked with is with the in dimensional Oriented makes upon what compact manifold and Of dimensions The Tonto Basin Basin defined simply the 1 . cases of the talks So I history that In a beach Figures you have the year the year of the bond was based here and now you want compact Viet so you get something like it's now there's some immunity be funded important facts that I want so well that I never want to point out the first one is so obvious from the picture namely that complement of the based And in the Thomas based in this 1 . com rectification that forms to the point of this is just follow the alliance Ali Khamenei Final Basis The horse on the nite of the new just fall out We in a continuous in favor that since Tom places like a local station of The year On the body Not only did And on the base based on loans still say the same thing I want to point out is You Tom isomorphous which Me I've home on the base Saying CIA trust in full Monty of the Toms and then finally the most important thing for from my purpose is to upon socalled country song for that matter So now we we could say that D dimensional manifold In A new interest fees based on manifold before we all we look services but this is what's needed more Dual context so a lot of symbolically manifold by neighborhood Opened Norwich you amount that a man Drawn here Mr. said to isomorphic of For course just expand nearly out these material that's what makes but you just to expand that out and into the food normal so that all want This is really the same No 1 of On Of The year of the embedding of Indian I interest now when you have scissors so you have Old stuff safe easy on Do I do You European based and now they want . com predication should met the other ways you should say a bruising outside The 2 be into the point and affinity So this and that was the 1 part company faces cleared in space that's a year that's severe dimension and trustee of the sea Fears of man once have bidding And you have a tube abounded then this Map the forger song For that That from the severe into the Tonto Basin that matter In some ways of a convenient way Of their displays all of the hunt in enormous structure of this In baby show of force It there's also may have an eviction if you have an Athens was Tom based in make that transversal Association in in a manifold off and that correspond which 50 years ago was used by some jargon and Show Manifolds optical What I want it back to that Show Now I want to be a starter Manifolds embedded in He knows in In Euclidean space and pick Euclidean spaces and I want to make that in the remain now want to enter into can't make that up with a year With this the space of West men So I a space West man in West he of iron must be seen in the face of these stuff Bases The European space I trust these Chief Well that face Senior bases Of the mentioned beat United interest this autumn They knew you can't say the fears of an element you in a nite in 1st and hand A Dedham softly and the best man And then you so that you with A mail If Start to be That's an individual bond over the West man in not a sixday plane that now we have a situation where we have what we have The manifold In Bay this is another It is not closed BAT and leave the peak the nor to wear that section of the unique from Mason still We can get Without delay Without changing in saying nothing has that situation and the And we take a point now In Indian Point excelled namely that of course we have the tendon fiber at that
34:07
Point that it'd be mental softly base so that the tank space The TX and is an element in the West man And if it sees you out He cited 2 well that states Over unique element in the area and not signify not Woods Lies over the point 8 in Then the Edelman view of the This List Fight in the jewel that's In all of this on a new and in That Just justifying so all in all we get and that you should for that matter a mean and the into incidents on the basis of this universal in the mental will then begin a map From the published Since NHTSA's song based on duty in her soul or fear of theater We get an element of Hold the interest before the base On On a visit on space by I means its base of continues from It's must be into the hands of the Tomahawk based what's the point of infinity Meaning this At the point of dignity In The child so we signed ahead Southland like didn't make it a man like death or a mail should say that if I have a soft manifold trust Chu orders and not important if you could be costly Yeah Mean they unique optative summation Now I could take the conviction on more these Tom spaces As in various that's what hold banks will supplant did and And this is your face Of the year on the on these Tom spaces which I got into here in a month and take it Limited they sit inside None union are director commitment of those and that's what we call the infinite space corresponding to that's pixel that Space but That's the kind of agents of bid Good to analyze And break Far and Maybe it should also say that these bases with Rice like that nite If you were if you think of the space between a space and who then these bases The Infiniti in that's like being groups in in there in the sale of all or spaces for now the still that Michael vise tool of 40 years ago is that that had gone now from a from top It this limit of all of us Of the of all of these Look down Tom spaces in the name of that induces Office In call monthly into In the Minnesota River Basin Police show And since these are indeed Opponents In in there and these in space he has this That And the media who book components in this faces A copy of the into wild Written these species that had assists An isomorphous millions will call Now We did we only knew that energy chart worse The market Of vessel shows a year Still the So there paying would show the to this state for monthly on my own Yeah that's it Nominated for Satan different ways we already seeing that Told that that the vessel home market the model to be interested in is to say this is stable Monte on the map and fast which which voters at home on Kamins but what we exited through it in in December and things will result so therefore tossed a year the statement called on the map and ask who is simply the hallmark of the space will make Infiniti in Chile Chavez If the Would understand what the full months of the a of the right hand side is worse than we would give information about The vessel home after the Marsalis and said so much area and Internet in that breaks apart from that made the call mothers and babysitter who would best lead and have did not hear what the what This may be the best home on the right side It seems It's a In the Monty on duty Of the West man in a of true claims And a war in going on and that is That Paul classes Japan So The showed this Many Provides The true Mom puts Concerto Now let me hear that could let me let me removed Until 4 borders and series will 1st Ashes So estates and fear that it go where mostly interested in which show If we're talking about a tomato it but until a above 50 years ago on Wednesday the following charm and jacket and maybe more Consider the following a nations on Show closed oriented Do you mind as onedimensional land for or the exhibit and if is a compact manifold of 1 inch I wish Has told Barbara components while is
41:27
1 of the manifolds and the other 1 is manifold but Things always ended here Might 0 Mean Joe Obuasi orientation not want assigned there that there is Is that there is of film office in 1 into 1 boundary from Poland Don't be entered athletic Moss from the author a bomb ripped component so Until now of course is completely impossible to work so enumerated in all a bit more classes manifolds but with this About a paucity of recent it turns out that and computer Chad They classes as well for the The boss hoops The site borders Make it so do you might 1 so that his computer caffeinated by song and Billy also work contract particularly this Camassia talked about I should say it may be that that borders who had the advantage of small dimensions I mean after meaning mentioned no 1 to read into for a sensitive that's It's a complex predicts base of the real amends Full Now this just this definition doesn't really involved the more but I want to go back to reconsider surfaces where these Which was too Better and that Be orbit based the and bedding What if you more of his testifying based on data more so now I want to take a few more Of the objects of the of these manifolds into consideration defined a category I'd replace Iast manifolds By embedded wants so written down what do you want the objects here and maybe at the same time put on his picture Receive in the picture so also Those embedded in 1 place and I have Also made this case Also embedded in another In the men's plays amorphous Between these This is simply a again and embedded in this case and the bed surface which goes from the from from from what lies That's fine by me and not by 8 not so immersed life's defined by the 8 1 which so that's Sort funny categories this invaded borders but The picks out their composition Just Taking union not this Each time you have to have the category which will category with the objects and both total set off more Jones said Did you could refer this defined space others so I'm just writing that Now it is matter of fact on May 1st surged it's that Is a him That cost once filled once simply Testifying place showed the point in this classified based pct But it's it corresponds to these 2 of the year These objects in the cabin if I have 2 the category That is composer all the negative to same place in space it said so build on based simply by By looking at The composition of the NO Like that a new some examples Of that construction if the optics assistant just A single point and the more on that point is proved he then this construction simply gives a good version of the classifying space being G for that's a space classified principal 5 on solid case But he was It was a bit more of a 50 minute or so of the existing based testifies These are the 1st surfaced on with fight of All of them 2 units G isn't doing this for this category of justify the pictures here at the end I think the composer of that space and that's just the A considered by buying from John solid city name is yeast Acer purports plot Now it's said This fear I 1st want to stay here is see Woods advances Gang of Four that I that I started with visits We can begin to choke the full based also written down here we can determine written down what do basis point of the base of the B of the categories and that space as defined before Which was which was Look base Of these universal want rules over the West many in Tibet's That's a 1st fish I want Concha These pervasive and that this aboard category that were that Show that That comes from from fees series went 1 worldwide was not considered before But But sometimes Shirley evasion come from other sources so would you could say that it can't It is simply a font of from this category David who borders only in some categories of Hilbert spaces and they still might Be of some help in trying to understand various Various these series but that the list Yeah Have to be worked out This Earlier potentially gives you information about film not Because of losses In this category maybe a should foot The level of the picture on again The more office
49:10
In the in this category was that If this big that is The course of the lessons of the of the of the of the space it gives you that if you a once in place in peak MIG all and saved it to occur in peak at so this Map from the more Paid into the base of the Gamache because if you have a home office all passenger space in the year in bid to winners of that More office unless they the the same element in there in the board room and you could just can't make some basic point and that way you get a map From the space of Aum office All of these embedded surfaces in a complete in space into the base Of the of the category So what could ask Is there some peak A WGU sold that this They some authors that was the year that But that was the same Different Mason look as tho there was a union but it was It contains These classifying spaces of a office so this a man here and can we find and not be being sold that Those Dodge manifold so so that this map is closed Being an equivalent annex to pass the bill is to provide access match in the year They It there There is a case where its services We consider when there where the borders Each of them Here I in the picture nothing similar only in the union had reason that of course is 1 of the wonders of 1 of the of the real problems In this in the subject I would like to go back a little bit now Chilworth Have stability Sale of putting it So now we consider services at me the boundary We had been bound say it A menorah industry so again we can take the more The more who of of that surface which has yet been busy on the boundary and we can take it the who will compose and that's course the mapping cast who can achieve and again you have a gun like theories saw for for a for both for closer offices which says The 2 components are Retractable shows that The classifying spaces homophobic prudently they can perform into weeks of not what happens civil wars than if you have a surface of Jews would be bothered composed even at the new Panetta
52:47
As of this year will win 1 more genius just who would on or you could also shows off that The shortest show you have It did more office of suffers indicated Because it's the identity of the bomber UBS You get a bit a few more of the a meeting of dish do want saying simply by adding the identity So this is a match like these All we could the maps composed and then were in there and then It is the these match In Jews isomorphous on fourmonth means will call monthly interest rate So now you could define a a B of the MNC We should be the directly in way he bond Doing it keep doing on the surface Like to keep these things to run here and there you would think that The union of the limits that would limit aboard the space for that began and seemed to be and the car model that space that is what I Defined before war Stated call muscle Or to make use of that 1 has work defined as a subcategory on this Category of data services The category has same number of so demands onedimensional manifolds toward the case surfaces and that the suffocated but it has fueled more named the more you consider only has the property that connected component has some
54:54
I Will the boundaries so you could these things he had postal and not enough it turns out that Show Red Yeah That this stuff category has to say Pleasant space object information so of this A survey and B To get us said the that could based on the use of this Mistreated Of the cast of MySpace State the category It Teakwood true is the same as Look down on base Which The best homeopathy of that put moment But the coverage for us this was not the way that there My advice and and I written to approved the sale of this but there it provides a new proof of the The That this of commodity Isomorphous between between this This base That might be whose lot State home wanted a they call comedy of the on the must 1st base and in and in this new face with Bush here on I would like to alert them Sir See Gywn preacher was us there some less
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