Acta Mathematica Vietnamica

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Twisted Alexander Polynomials and Ideal Points Giving Seifert Surfaces
Takahiro Kitayama

 

Abstract

The coefficients of twisted Alexander polynomials of a knot induce regular functions of the SL2(C) -character variety. We prove that the function of the highest degree has a finite value at an ideal point which gives a minimal genus Seifert surface by Culler–Shalen theory. It implies a partial affirmative answer to a conjecture by Dunfield, Friedl, and Jackson.

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