Logic Seminar
Kathryn Mann
UC Berkeley
Automatic continuity of homeomorphism groups
Abstract: When is an abstract homomorphism between topological groups forced to be continuous? In geometry, there are several examples of this kind of rigidity or "automatic continuity" using extra assumptions on the groups and homomorphisms involved. Richer algebraic structures -- e.g. Banach algebras, Polish groups -- often exhibit automatic continuity with very few strings attached. The group of homeomorphisms of a compact manifold is one such example. In this talk, I'll show that any homomorphism from Homeo(M) to any other separable topological group is necessarily continuous. The proof combines ideas of Rosendal, standard tricks in automatic continuity, and arguments in manifold topology.
Tuesday March 17, 2015 at 4:00 PM in SEO 636