Coarse cubical rigidity
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908907393253376 |
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| author | Fioravanti, Elia Levcovitz, Ivan Sageev, Michah |
| author_facet | Fioravanti, Elia Levcovitz, Ivan Sageev, Michah |
| contents | We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this property.
For all graph products of finite groups and for Coxeter groups with no irreducible affine parabolic subgroups of rank $\geq 3$, we show that all automorphism preserve the coarse median structure induced, respectively, by the Davis complex and the Niblo-Reeves cubulation. As a consequence, automorphisms of these groups have nice fixed subgroups and satisfy Nielsen realisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11418 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Coarse cubical rigidity Fioravanti, Elia Levcovitz, Ivan Sageev, Michah Group Theory Geometric Topology Metric Geometry We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this property. For all graph products of finite groups and for Coxeter groups with no irreducible affine parabolic subgroups of rank $\geq 3$, we show that all automorphism preserve the coarse median structure induced, respectively, by the Davis complex and the Niblo-Reeves cubulation. As a consequence, automorphisms of these groups have nice fixed subgroups and satisfy Nielsen realisation. |
| title | Coarse cubical rigidity |
| topic | Group Theory Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2210.11418 |