Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910617662652416 |
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| author | Cheetham-West, Tamunonye |
| author_facet | Cheetham-West, Tamunonye |
| contents | We show that hyperbolic four-punctured $S^2-$bundles over $S^1$ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered hyperbolic 3-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle Cheetham-West, Tamunonye Geometric Topology Group Theory 57K32 (Primary) 20E18, 57K20 (Secondary) We show that hyperbolic four-punctured $S^2-$bundles over $S^1$ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered hyperbolic 3-manifold. |
| title | Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle |
| topic | Geometric Topology Group Theory 57K32 (Primary) 20E18, 57K20 (Secondary) |
| url | https://arxiv.org/abs/2308.00266 |