
George Domat
University of Michigan
Title
Classification of Stable Surfaces with respect to Automatic Continuity
Abstract
Topological groups often exhibit lots of interplay between their algebraic and topological structures. A stark example of this is the automatic continuity property: A topological group has the automatic continuity property if every (algebraic) homomorphism to any other separable group is continuous. We provide a complete classification of when the homeomorphism group of a stable surface has the automatic continuity property. Towards this classification, we provide a general framework for proving automatic continuity for groups of homeomorphisms. This is joint work with Mladen Bestvina and Kasra Rafi.