On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the $A$-polynomial

Fuente: arXiv
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Autor principal: Xu, Xiaoyu
Formato: Preprint
Publicado: 2025
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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