Topology Seminar: Groups acting on the circle

Seminar | January 11 | 4:10-5 p.m. | 740 Evans Hall | Note change in location

 Kathryn Mann, UC Berkeley

 Department of Mathematics

Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic and natural question from geometric topology, but also a very difficult one – even in the case where M is the circle, and G is a familiar, finitely generated group like the fundamental group of a surface.

In this talk, I'll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others. I'll describe some connections between this theory and themes in topology and dynamics (like classifying foliations), some previous work and current open problems, and indicate a new approach coming from recent joint work with C. Rivas. This will be a colloquium-style talk, and should be broadly accessible.