Smoothing countable group actions on metrizable spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913539879337984 |
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| author | Choi, Inhyeok Kim, Sang-hyun |
| author_facet | Choi, Inhyeok Kim, Sang-hyun |
| contents | We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenstädt regarding finitely generated groups, and our proof is based upon her idea. This also gives a simple proof of a theorem due to Deroin, Kleptsyn and Navas regarding one-manifolds. We also establish an analogous result for closed subgroups of locally compact groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smoothing countable group actions on metrizable spaces Choi, Inhyeok Kim, Sang-hyun Group Theory Dynamical Systems We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenstädt regarding finitely generated groups, and our proof is based upon her idea. This also gives a simple proof of a theorem due to Deroin, Kleptsyn and Navas regarding one-manifolds. We also establish an analogous result for closed subgroups of locally compact groups. |
| title | Smoothing countable group actions on metrizable spaces |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2410.06077 |