The structure of relatively hyperbolic groups in convex real projective geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908728929812480 |
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| author | Islam, Mitul Zimmer, Andrew |
| author_facet | Islam, Mitul Zimmer, Andrew |
| contents | In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a characterization of such groups in terms of the existence of an invariant collection of closed unbounded convex subsets with good isolation properties. This is a real projective analogue of results of Hindawi-Hruska-Kleiner for ${\rm CAT}(0)$ spaces. We also obtain an equivariant homeomorphism between the Bowditch boundary of the group and a quotient of the ideal boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16596 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The structure of relatively hyperbolic groups in convex real projective geometry Islam, Mitul Zimmer, Andrew Geometric Topology Differential Geometry In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a characterization of such groups in terms of the existence of an invariant collection of closed unbounded convex subsets with good isolation properties. This is a real projective analogue of results of Hindawi-Hruska-Kleiner for ${\rm CAT}(0)$ spaces. We also obtain an equivariant homeomorphism between the Bowditch boundary of the group and a quotient of the ideal boundary. |
| title | The structure of relatively hyperbolic groups in convex real projective geometry |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2203.16596 |