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Stability of hyperbolic groups acting on their boundaries
A hyperbolic group \Gammaacts by homeomorphisms on its Gromov boundary\partial \Gamma. We use a dynamical coding of boundary points to show that such actions aretopologically stablein 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 \Gammais 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}.
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- Award ID(s):
- 1933598
- PAR ID:
- 10617396
- Publisher / Repository:
- EMS Press
- Date Published:
- Journal Name:
- Groups, Geometry, and Dynamics
- ISSN:
- 1661-7207
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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