A hyperbolic group acts on its Gromov boundary by homeomorphisms. In recent work with Jason Manning, we showed that for groups with sphere boundary, the boundary action is rigid in the sense of topological dynamics: any sufficiently small perturbation is semi-conjugate to the original action. In ongoing work also with Teddy Weisman, we are extending this result to all hyperbolic groups, using a coding argument in the spirit of Sullivan. This talk will introduce the rigidity problem and describe some of the tools towards the proof.
Fanny Kassel
