|DATE||November 25 (Wed), 2020|
|TITLE||Stability for hyperbolic groups acting on their boundaries.|
|ABSTRACT||A hyperbolic group acts naturally by homeomorphisms on its Gromov boundary. The theme of this talk is to say that, in many cases, such an action has very rigid dynamics.
Jonathan Bowden and I studied a special case of this, showing if G is the fundamental group of a compact, negatively curved Riemannian manifold, then the action of G on its boundary is what dynamicists call "topologically stable", meaning that small perturbations contain the same dynamical information as the original action. In new work with Jason Manning, we extend this to hyperbolic groups with sphere boundary, using large-scale geometric techniques. I will give some of the history of this problem and a sketch of the techniques used in the proof.
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