Departmental Bulletin Paper Twisted Alexander Polynomials and Incompressible Surfaces Given by Ideal Points

Kitayama, Takahiro

22 ( 3 ) 2015-07-15 , Graduate School of Mathematical Sciences, The University of Tokyo , Department of Mathematics, Tokyo Institute of Technology
We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a 1st cohomology class of a 3-manifold the coefficients of twisted Alexander polynomials induce regular functions on the SL2(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.

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