Twisted Alexander Polynomials and Incompressible Surfaces Given by Ideal Points
Vol. 22 (2015), No. 3, Page 877–891.
Kitayama, Takahiro
Twisted Alexander Polynomials and Incompressible Surfaces Given by Ideal Points
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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 $SL_2(\mathbb C)$-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.
Keywords: Twisted Alexander polynomial, Reidemeister torsion, character variety.
Mathematics Subject Classification (2010): Primary~57M27; Secondary~57Q10.
Mathematical Reviews Number: MR3408076
Received: 2014-06-30