On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the $A$-polynomial
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918176793559040 |
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| author | Xu, Xiaoyu |
| author_facet | Xu, Xiaoyu |
| contents | We prove that any isomorphism between the profinite completions of the fundamental groups of two cusped finite-volume hyperbolic 3-manifolds is regular and peripheral regular. As an application, we show that the $A$-polynomial of prime knots in $S^3$ is a profinite invariant, up to possible mirror image. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the $A$-polynomial Xu, Xiaoyu Geometric Topology Group Theory Primary: 20E18, 20J06, 57K14, 57K31, 57M10, Secondary: 57K10, 57K32, 57M05, 57M50 We prove that any isomorphism between the profinite completions of the fundamental groups of two cusped finite-volume hyperbolic 3-manifolds is regular and peripheral regular. As an application, we show that the $A$-polynomial of prime knots in $S^3$ is a profinite invariant, up to possible mirror image. |
| title | On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the $A$-polynomial |
| topic | Geometric Topology Group Theory Primary: 20E18, 20J06, 57K14, 57K31, 57M10, Secondary: 57K10, 57K32, 57M05, 57M50 |
| url | https://arxiv.org/abs/2506.21105 |