Twisted Alexander polynomials and ideal points giving Seifert surfaces

Abstract

The coefficients of twisted Alexander polynomials of a knot induce regular functions of the $S{L}_2(\mathbb{C})$-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.

7 pages, to appear in a special issue of Acta Mathematica Vietnamica for the proceedings of the conference "The Quantum Topology and Hyperbolic Geometry" (Nha Trang, Vietnam, May 13-17, 2013)

Cited by in corpus (1)

• Twisted Alexander polynomials and incompressible surfaces given by ideal points