Geometric Analysis and Topology Seminar

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Rigidity of hyperbolic groups acting on their boundaries

Speaker: Kathryn Mann, Cornell

Location: Warren Weaver Hall 512

Videoconference link: https://nyu.zoom.us/j/95759976381

Date: Friday, March 31, 2023, 11 a.m.

Synopsis:

Abstract:  Every hyperbolic group has a compactification "at infinity" by its Gromov boundary, a topological space on which the group acts naturally by homeomomrphisms.  In joint work with Jason Manning and Teddy Weisman (building on work with Jonathan Bowden), we show that these actions are stable in the sense of topological dynamics.   One of our proof strategies has since been adapted by Connell, Islam, Nguyen and Spatzier to study rigidity for actions of cocompact lattices in semisimple lie groups on their boundaries, and another by Manning--Weisman and myself to treat the relatively hyperbolic case.   I'll give you an introduction and motivation for these problems, and some cartoons of the main ideas of proof.