Topology Seminar

A hyperbolic group acts naturally by homeomorphisms on its Gromov boundary. An important example is the action of the fundamental group of a compact negatively curved manifold on the sphere at infinity of it's universal cover.

This talk is about recent joint work with Jonathan Bowden and later (work in progress) with Jason Manning, where we show these actions are rigid, or stable under perturbation. With Bowden, we show this for manifold fundamental groups using ideas around geodesic flow. With Manning, we use only geometric group theory, generalizing the theorem to Gromov-hyperbolic groups with sphere boundary. I will give some of the history and motivation for this problem and sketch the techniques used in the proofs. Speaker(s): Kathryn Mann (Cornell University)