Profinite rigidity for twisted Alexander polynomials-Reference-Cited by-同舟云学术

Profinite rigidity for twisted Alexander polynomials

Published:2020-07-11 Issue:771 Volume:2021 Page:171-192
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Ueki Jun¹

Affiliation:

1. Department of Mathematics , School of System Design and Technology , Tokyo Denki University , 5 Senju Asahi-cho, Adachi-ku, 120-8551 , Tokyo , Japan

Abstract

Abstract We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a ℤ

{{\mathbb{Z}}}

-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2020-0014/pdf

Reference58 articles.

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3. M. Boileau and S. Friedl, The profinite completion of 3-manifold groups, fiberedness and Thurston norm, preprint (2015), https://arxiv.org/abs/1505.07799

4. published in: What's next?: The mathematical legacy of William P. Thurston, Ann. of Math. Stud. 363, Princeton University Press, Princeton (2020), 21-44.

5. M. R. Bridson and A. W. Reid, Profinite rigidity, fibering, and the figure-eight knot, arXiv:1505.07886, preprint (2015), https://arxiv.org/abs/1505.07886

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1. Twisted Iwasawa invariants of knots;Mathematische Nachrichten;2023-11-09

2. Finite Quotients, Arithmetic Invariants, and Hyperbolic Volume;Peking Mathematical Journal;2023-08-17

3. Erratum to Profinite rigidity for twisted Alexander polynomials (J. reine angew. Math. 771 (2021), 171–192);Journal für die reine und angewandte Mathematik (Crelles Journal);2022-01-06