BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Peter Haine (MIT)
DTSTART:20210503T203000Z
DTEND:20210503T213000Z
DTSTAMP:20260423T024540Z
UID:MITTop/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/31/">
 On the homotopy theory of stratified spaces</a>\nby Peter Haine (MIT) as p
 art of MIT topology seminar\n\n\nAbstract\nA natural question arises when 
 working with intersection cohomology and other stratified invariants of si
 ngular manifolds: what is the correct stable homotopy theory for these inv
 ariants to live in? But before answering that question one first has to id
 entify the correct unstable homotopy theory of stratified spaces. The exit
 -path category construction of MacPherson\, Treumann\, and Lurie provides 
 functor from suitably nice stratified topological spaces to “abstract st
 ratified homotopy types” — ∞-categories with a conservative functor 
 to a poset. Work of Ayala–Francis–Rozenblyum even shows that their con
 ically smooth stratified topological spaces embed into the ∞-category of
  abstract stratified homotopy types. In this talk\, we explain some of our
  work which goes further and produces an equivalence between the homotopy 
 theory of all stratified topological spaces and these abstract stratified 
 homotopy types.\n
LOCATION:https://researchseminars.org/talk/MITTop/31/
END:VEVENT
END:VCALENDAR