## Twisted Alexander Polynomials and Incompressible Surfaces Given by Ideal Points

J. Math. Sci. Univ. Tokyo
Vol. 22 (2015), No. 3, Page 877–891.

Kitayama, Takahiro
Twisted Alexander Polynomials and Incompressible Surfaces Given by Ideal Points
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 $SL_2(\mathbb C)$-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.