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arXiv · 2402.06144

Topological stability of relatively hyperbolic groups acting on their boundaries

Kathryn Mann·Jason Fox Manning·Theodore Weisman
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Abstract

We prove a topological stability result for the actions of hyperbolic groups on their Bowditch boundaries. More precisely, we show that a sufficiently small perturbation of the standard boundary action, if assumed on each parabolic subgroup to be a perturbation by semi-conjugacy, is in fact always globally semi-conjugate to the standard action. This proves a relative version of the main result of arXiv:2206.14914. The assumption of control on the perturbation of parabolics is necessary.

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Kathryn Mann, Jason Fox Manning, Theodore Weisman. 2024-02-09. Topological stability of relatively hyperbolic groups acting on their boundaries. https://arxiv.org/abs/2402.06144

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