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SUMMARY:The Exit Path ∞-Category of the Reductive Borel-Serre Compactifi
 cation
DTSTART:20200428T101500
DTEND:20200428T111500
DTSTAMP:20260924T080111Z
UID:caf569d6fad661aac5a2b72b16b1d0e5be2d6ef160bf215e178671c0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mikala Ørsnes Jansen\, Københavns Universitet\n\nFor neat a
 rithmetic groups Γ ≤ SLn(ℤ)\, the locally symmetric space X associa
 ted with Γ provides a nice model for the classifying space BΓ : it is
  a smooth manifold and thus allows for the study of the discrete group to 
 move into the geometric realm. Unfortunately\, X is very rarely compact. T
 o remedy this\, Borel and Serre in 1973 constructed a compact manifold wit
 h corners into which X embeds as the interior. It is now known as the Bor
 el-Serre compactification of X\, and it enabled Borel to calculate the ra
 nks of the algebraic K-groups Ki(ℤ). For some purposes\, however\, the B
 orel-Serre compactification is ``too big''. Motivated by an interest in L2
 -cohomology\, Zucker introduced another compactification of X in 1982\, la
 ter coined the reductive Borel-Serre compactification. It is defined as a
  quotient of the Borel-Serre compactification and is no longer a manifold 
 with corners. It does\, however\, come equipped with a natural stratificat
 ion. We set out to understand this stratified space by determining its ex
 it path ∞-category. This is an analogue for stratified spaces of the fu
 ndamental ∞-groupoid for topological spaces: it provides information no
 t only about the individual strata but also about how these strata are ``g
 lued'' together. We show that the reductive Borel-Serre compactification i
 s in some sense a K(π\,1) of stratified spaces by showing that its exit p
 ath ∞-category is equivalent to the nerve of a 1-category. Moreover\, s
 ome interesting questions arise when looking back at algebraic K-theory.\n
 This is joint work with Dustin Clausen.\n\n 
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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