Twisted Alexander polynomials and incompressible surfaces given by ideal points

Abstract

We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions on the $S{L}_2(\mathbb{C})$-character variety. We prove that if an ideal point gives a Thurston norm minimizing non-separating surface dual to the cohomology class, then the regular function of the highest degree has a finite value at the ideal point.

10 pages, to appear in "The special issue for the 20th anniversary", the Journal of Mathematical Sciences, the University of Tokyo

References in corpus (2)

• Poincaré duality and degrees of twisted Alexander polynomials
• Twisted Alexander polynomials and ideal points giving Seifert surfaces