Profinite rigidity for twisted Alexander polynomials

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

Abstract

<jats:title>Abstract</jats:title><jats:p>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<jats:inline-formula id="j_crelle-2020-0014_ineq_9999"><jats:alternatives><m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>ℤ</m:mi></m:math><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2020-0014_eq_0611.png" /><jats:tex-math>{{\mathbb{Z}}}</jats:tex-math></jats:alternatives></jats:inline-formula>-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.</jats:p>

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