Twisted Alexander vanishing order of knots

Katsumi Ishikawa; Takayuki Morifuji; Masaaki Suzuki

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arXiv · 2310.10936

Twisted Alexander vanishing order of knots

Katsumi Ishikawa·Takayuki Morifuji·Masaaki Suzuki

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Abstract

Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the twisted Alexander vanishing order of a knot to be the order of the smallest finite group such that the corresponding twisted Alexander polynomial is zero. In this paper, we show its basic properties, and provide several explicit values for knots with $10$ or fewer crossings. Moreover, we characterize a finite group admitting the zero-twisted Alexander polynomial.

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Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki. 2023-10-17. Twisted Alexander vanishing order of knots. https://arxiv.org/abs/2310.10936

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