Stability of hyperbolic groups acting on their boundaries
Year: 2025
Type: article
Abstract: A hyperbolic group \Gamma acts by homeomorphisms on its Gromov boundary \partial \Gamma . We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an extension of) the standard boundary action. This result was previously known in the special case that \partial \Gamma is a topological sphere. Our proof here is independent and gives additional information about the semi-conjugacy in that case. Our techniques also give a new proof of global stability when \partial \Gamma = S^{1} .
Source: Groups Geometry and Dynamics
DOI: 10.4171/ggd/869
Institutions: Cornell University, University of Michigan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408525332