Kathryn Mann : Automatic continuity of homeomorphism groups

Posted by Kostyantyn Slutskyy , part of the Logic Seminar.

At

March 17, 2015, 4 p.m.

In

SEO 636

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.