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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.12837 |
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| _version_ | 1866913993948397568 |
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| author | Hao, Yanlong |
| author_facet | Hao, Yanlong |
| contents | In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently large $p$. As an application, we prove that any isometric action of a group with the fixed point property $F_\infty$ on a good hyperbolic space must have a bounded orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12837 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Groups that (do not) act isometrically on hyperbolic spaces Hao, Yanlong Group Theory In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently large $p$. As an application, we prove that any isometric action of a group with the fixed point property $F_\infty$ on a good hyperbolic space must have a bounded orbit. |
| title | Groups that (do not) act isometrically on hyperbolic spaces |
| topic | Group Theory |
| url | https://arxiv.org/abs/2212.12837 |