Twisted Alexander polynomials and ideal points giving Seifert surfaces

Takahiro Kitayama

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arXiv · 1406.4626

Twisted Alexander polynomials and ideal points giving Seifert surfaces

Takahiro Kitayama

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Abstract

The coefficients of twisted Alexander polynomials of a knot induce regular functions of the $SL_2(\mathbb{C})$-character variety. We prove that the function of the highest degree has a finite value at an ideal point which gives a minimal genus Seifert surface by Culler-Shalen theory. It implies a partial affirmative answer to a conjecture by Dunfield, Friedl and Jackson.

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Takahiro Kitayama. 2014-06-18. Twisted Alexander polynomials and ideal points giving Seifert surfaces. https://arxiv.org/abs/1406.4626

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