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Seminar
FIELD Math:Topology
DATE February 17 (Thu), 2022
TIME 09:00-10:30
PLACE Online
SPEAKER Nariman, Sam
HOST Kim, Sang-hyun
INSTITUTE Purdue University
TITLE On perfectness of PL homeomorphisms of surfaces
ABSTRACT ONLINE
https://visgat.cayley.kr

Diffeomorphism groups and PL homeomorphisms have similar algebraic properties. From the point of view of foliation theory, they both support characteristic classes known as Godbillon-Vey classes and also they both exhibit the local indicability property thanks to Thurston and Calegari-Rolfsen respectively. Thurston and Mather showed that Diff^r_0(M), the group of C^r diffeomorphisms of a closed manifold M that are isotopic to the identity, is perfect (in fact simple) for r≠ dim(M)+1. On the other hand, Epstein proved that PL_0(S^1) and PL_c(R) are perfect groups and left the question of perfectness of PL homeomorphisms of higher dimensional PL manifolds open. In this talk, we explain a homotopy theoretic approach to prove that PL homeomorphisms of surfaces are perfect.
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