Product separability for special cube complexes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918248521400320 |
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| author | Shepherd, Sam |
| author_facet | Shepherd, Sam |
| contents | We prove that if a group $G$ admits a virtually special action on a CAT(0) cube complex, then any product of convex-cocompact subgroups of $G$ is separable. Previously, this was only known for products of three subgroups, or in the case where $G$ is hyperbolic, or in some other more technical cases with additional assumptions on the subgroups (plus these previous results assume that the action of $G$ is cocompact). We also provide an application to the action of a virtually special cubulated group on its contact graph (and to some other actions of cubulated groups on graphs). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Product separability for special cube complexes Shepherd, Sam Group Theory 20F65 (Primary) 20F67, 20E26, 57M10 (Secondary) We prove that if a group $G$ admits a virtually special action on a CAT(0) cube complex, then any product of convex-cocompact subgroups of $G$ is separable. Previously, this was only known for products of three subgroups, or in the case where $G$ is hyperbolic, or in some other more technical cases with additional assumptions on the subgroups (plus these previous results assume that the action of $G$ is cocompact). We also provide an application to the action of a virtually special cubulated group on its contact graph (and to some other actions of cubulated groups on graphs). |
| title | Product separability for special cube complexes |
| topic | Group Theory 20F65 (Primary) 20F67, 20E26, 57M10 (Secondary) |
| url | https://arxiv.org/abs/2412.08248 |