Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917410696593408 |
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| author | Groves, Daniel Stark, Emily Walsh, Genevieve S. Whyte, Kevin |
| author_facet | Groves, Daniel Stark, Emily Walsh, Genevieve S. Whyte, Kevin |
| contents | We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13898 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric Groves, Daniel Stark, Emily Walsh, Genevieve S. Whyte, Kevin Group Theory Geometric Topology 20F65, 51F30, 20F18, 20F67 We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line. |
| title | Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric |
| topic | Group Theory Geometric Topology 20F65, 51F30, 20F18, 20F67 |
| url | https://arxiv.org/abs/2604.13898 |