Stability for hyperbolic groups acting on boundary spheres

2021/04/02 by Kathryn Mann, Jason Fox Manning, Mann, Kathryn +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2104.01269

openalex publication_date 2021/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We show that if this boundary is a topological n-sphere the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard boundary action.

Related

• Stability of hyperbolic groups acting on their boundaries
• Topological stability of relatively hyperbolic groups acting on their boundaries
• Shadowing of actions of hyperbolic groups on their boundaries
• C⁰ stability of boundary actions and inequivalent Anosov flows
• Boundary actions of lattices and C⁰ local semi-rigidity