Twisted Alexander Polynomials and Ideal Points Giving Seifert Surfaces

Abstract

The coefficients of twisted Alexander polynomials of a knot induce regular functions of the \(SL_{2}(\mathbb {C})\)-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.