Twisted Alexander polynomials and incompressible surfaces given by ideal points

Takahiro Kitayama

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arXiv · 1412.4483

Twisted Alexander polynomials and incompressible surfaces given by ideal points

Takahiro Kitayama

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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.

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BibTeX RIS

Takahiro Kitayama. 2014-12-15. Twisted Alexander polynomials and incompressible surfaces given by ideal points. https://arxiv.org/abs/1412.4483

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