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Profinite rigidity for twisted Alexander polynomials

  • Jun Ueki EMAIL logo
Published/Copyright: July 11, 2020

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 -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.

Award Identifier / Grant number: JP19K14538

Funding statement: This work was partially supported by JSPS KAKENHI Grant Number JP19K14538.

Acknowledgements

The author would like to express his sincere gratitude to Léo Bénard, Michel Boileau, Frank Calegari, Yuichi Hirano, Teruhisa Kadokami, Takenori Kataoka, Tomoki Mihara, Yasushi Mizusawa, Alan Reid, Kenji Sakugawa, Ryoto Tange, Anastasiia Tsvietkova, and Yoshikazu Yamaguchi, people I met at CIRM in Luminy and at GAU in Göttingen, and anonymous referees of the previous articles and this article for useful comments and fruitful conversations.

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Received: 2019-11-26
Revised: 2020-04-29
Published Online: 2020-07-11
Published in Print: 2021-02-01

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