EVENT DETAILS AND ABSTRACT

Title: Extension problems for groups of diffeomorphisms
Speaker: Kathryn Mann
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

If M is a manifold with boundary dM, restricting an (isotopically trivial) diffeomorphism of M to its action of the boundary gives a surjective homomorphism from Diff_0(M) to Diff_0(dM). Does this map ever admit a section?

The answer is usually no, and the reasons are usually interesting. In this talk, we describe obstructions to sections Diff_0(dM) -> Diff_0(M) and in a number of cases obstructions to lifting finitely generated subgroups of Diff_0(dM) to groups of diffeomorphisms of M. Our methods range from the dynamical to the cohomological, and will be illustrated as much as possible with concrete examples.