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SUMMARY:Topology Seminar: Stratified homotopy theory
DTSTART:20180508T101500
DTEND:20180508T111500
DTSTAMP:20260504T081903Z
UID:b98b9ab32fc9a5121b4ceb6d15d0eb90e65e5b422eb2555d414334a5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sylvain Douteau (Université de Picardie)\nStratified spaces a
 ppear as natural objects in singularity theory. Goresky and MacPherson int
 roduced intersection cohomology to extend cohomological properties of clos
 ed manifolds to stratified spaces\, and it proved to be a powerful tool to
  study those objects. However\, intersection cohomology is not homotopy in
 variant\, rather it is invariant with respect to homotopies that "preserve
 " the stratification. This begs the question: does there exist a model cat
 egory of stratified spaces which reflects this stratified notion of homoto
 py\, and if so\, is intersection cohomology representable in it?\n\nWe ans
 wer the first part of this question using a simplicial model category of f
 iltered simplicial sets. As a category\, it is only the category of simpli
 cial sets over the classifying space of some fixed poset\, but as a preshe
 af category\, it inherits a model structure constructed using a natural cy
 linder object. We show that this category is simplicial\, then we get stra
 tified versions of Kan complexes and of homotopy groups that characterise 
 fibrations and weak equivalences.\n 
LOCATION:CM 1 113 https://plan.epfl.ch/?room==CM%201%20113
STATUS:CONFIRMED
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