Topological stability of relatively hyperbolic groups acting on their boundaries
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915492748328960 |
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| author | Mann, Kathryn Manning, Jason Fox Weisman, Theodore |
| author_facet | Mann, Kathryn Manning, Jason Fox Weisman, Theodore |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological stability of relatively hyperbolic groups acting on their boundaries Mann, Kathryn Manning, Jason Fox Weisman, Theodore Group Theory Geometric Topology 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. |
| title | Topological stability of relatively hyperbolic groups acting on their boundaries |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2402.06144 |