Automorphism groups of combinatorial Hantzsche-Wendt groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917567139938304 |
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| author | Lutowski, Rafał Szczepański, Andrzej Weidmann, Richard |
| author_facet | Lutowski, Rafał Szczepański, Andrzej Weidmann, Richard |
| contents | Combinatorial Hantzsche-Wendt groups were introduced by W. Craig and P.A. Linnell. Every such a group $G_n$, where $n$ is a natural number, encodes the holonomy action of any $n+1$-dimensional Hantzsche-Wendt manifold. $G_2$ is the fundamental group of the classical Hantzsche-Wendt manifold -- the only one $3$-dimensional oriented flat manifold with non-cyclic holonomy group. In this article, we describe the structure of the automorphism and of the outer automorphism groups of combinatorial Hantzsche-Wendt groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of combinatorial Hantzsche-Wendt groups Lutowski, Rafał Szczepański, Andrzej Weidmann, Richard Group Theory Primary: 20F28 Secondary: 20F05, 20E36, 20E06 Combinatorial Hantzsche-Wendt groups were introduced by W. Craig and P.A. Linnell. Every such a group $G_n$, where $n$ is a natural number, encodes the holonomy action of any $n+1$-dimensional Hantzsche-Wendt manifold. $G_2$ is the fundamental group of the classical Hantzsche-Wendt manifold -- the only one $3$-dimensional oriented flat manifold with non-cyclic holonomy group. In this article, we describe the structure of the automorphism and of the outer automorphism groups of combinatorial Hantzsche-Wendt groups. |
| title | Automorphism groups of combinatorial Hantzsche-Wendt groups |
| topic | Group Theory Primary: 20F28 Secondary: 20F05, 20E36, 20E06 |
| url | https://arxiv.org/abs/2401.05141 |