Colloquium: Diffeomorphism Groups and Foliations

Abstract: It has been known after Thurston that algebraic properties of diffeomorphism groups are related to geometric and dynamical properties of foliations. In particular, he used "the fragmentation property" of diffeomorphism groups to prove the simplicity and perfectness of diffeomorphism groups. As a result, he proved that 2-plane bundles are integrable up to homotopy. I will explain some of these ideas and their consequences for invariants of foliated bundles. If time permits, I will also explain how one can use Thurston's method backward to prove the simplicity of piecewise linear homeomorphisms of surfaces.

Host: Xiang Tang