Convex co-compact groups with one dimensional boundary faces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911971207544832 |
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| author | Islam, Mitul Zimmer, Andrew |
| author_facet | Islam, Mitul Zimmer, Andrew |
| contents | In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face in the ideal boundary has dimension at most one. We also introduce the "coarse Hilbert dimension" of a subset of a convex set and use it to characterize when a naive convex co-compact subgroup is word hyperbolic or relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05056 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Convex co-compact groups with one dimensional boundary faces Islam, Mitul Zimmer, Andrew Geometric Topology Differential Geometry Group Theory Metric Geometry 20F67, 20H10, 53A20, 57N16, 57S20 In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two if and only if each open face in the ideal boundary has dimension at most one. We also introduce the "coarse Hilbert dimension" of a subset of a convex set and use it to characterize when a naive convex co-compact subgroup is word hyperbolic or relatively hyperbolic with respect to a collection of virtually Abelian subgroups of rank two. |
| title | Convex co-compact groups with one dimensional boundary faces |
| topic | Geometric Topology Differential Geometry Group Theory Metric Geometry 20F67, 20H10, 53A20, 57N16, 57S20 |
| url | https://arxiv.org/abs/2104.05056 |