On a generalization of Cannon's conjecture for cubulated hyperbolic groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929384913371136 |
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| author | Bregman, Corey Incerti-Medici, Merlin |
| author_facet | Bregman, Corey Incerti-Medici, Merlin |
| contents | We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex, codimension-1 subgroups whose limit sets are locally flat subspheres. The proof is based on ideas used by Markovic in his work on Cannon's conjecture for cubulated hyperbolic groups with 2-sphere boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a generalization of Cannon's conjecture for cubulated hyperbolic groups Bregman, Corey Incerti-Medici, Merlin Geometric Topology Group Theory 57N16, 20F67 (primary), 20F65, 57N45, 57N35 (secondary) We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex, codimension-1 subgroups whose limit sets are locally flat subspheres. The proof is based on ideas used by Markovic in his work on Cannon's conjecture for cubulated hyperbolic groups with 2-sphere boundary. |
| title | On a generalization of Cannon's conjecture for cubulated hyperbolic groups |
| topic | Geometric Topology Group Theory 57N16, 20F67 (primary), 20F65, 57N45, 57N35 (secondary) |
| url | https://arxiv.org/abs/2406.08779 |