Actions of large finite groups on aspherical manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915338506993664 |
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| author | Serrano, Jordi Daura |
| author_facet | Serrano, Jordi Daura |
| contents | In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism group of the fundamental group of a closed connected aspherical manifold $M$, we prove that the homeomorphism group of $M$ is Jordan, we bound the discrete degree of symmetry of $M$ and obtain a rigidity result, and we study the number of stabilizers of finite group actions on $M$. Thereafter, we show that closed connected aspherical locally homogeneous spaces $H\setminus G/Γ$ satisfy the necessary hypothesis on the outer automorphism group of the fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Actions of large finite groups on aspherical manifolds Serrano, Jordi Daura Geometric Topology 57S17, 54H15, 22E40 In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism group of the fundamental group of a closed connected aspherical manifold $M$, we prove that the homeomorphism group of $M$ is Jordan, we bound the discrete degree of symmetry of $M$ and obtain a rigidity result, and we study the number of stabilizers of finite group actions on $M$. Thereafter, we show that closed connected aspherical locally homogeneous spaces $H\setminus G/Γ$ satisfy the necessary hypothesis on the outer automorphism group of the fundamental group. |
| title | Actions of large finite groups on aspherical manifolds |
| topic | Geometric Topology 57S17, 54H15, 22E40 |
| url | https://arxiv.org/abs/2407.13602 |