Twisted Alexander polynomials and ideal points giving Seifert surfaces
Geometric Topology
2014-06-19 v1
Abstract
The coefficients of twisted Alexander polynomials of a knot induce regular functions of the -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.
Cite
@article{arxiv.1406.4626,
title = {Twisted Alexander polynomials and ideal points giving Seifert surfaces},
author = {Takahiro Kitayama},
journal= {arXiv preprint arXiv:1406.4626},
year = {2014}
}
Comments
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)