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| 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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