Detecting embedded surfaces using finite quotients
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910067740114944 |
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| author | Cheetham-West, Tam Le, Khanh |
| author_facet | Cheetham-West, Tam Le, Khanh |
| contents | We give conditions on a Haken hyperbolic rational homology three sphere that imply that any other 3-manifold with profinitely equivalent fundamental group must also be Haken. In the appendix, we show that a regular finite-sheeted cover of an aspherical integral homology three-sphere with positive first Betti number must have first Betti number at least four. We also show that this lower bound is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Detecting embedded surfaces using finite quotients Cheetham-West, Tam Le, Khanh Geometric Topology 57K32 We give conditions on a Haken hyperbolic rational homology three sphere that imply that any other 3-manifold with profinitely equivalent fundamental group must also be Haken. In the appendix, we show that a regular finite-sheeted cover of an aspherical integral homology three-sphere with positive first Betti number must have first Betti number at least four. We also show that this lower bound is sharp. |
| title | Detecting embedded surfaces using finite quotients |
| topic | Geometric Topology 57K32 |
| url | https://arxiv.org/abs/2603.22543 |