Twisted Alexander vanishing groups of knots

Katsumi Ishikawa; Takayuki Morifuji; Masaaki Suzuki

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arXiv · 2605.13291

Twisted Alexander vanishing groups of knots

Katsumi Ishikawa·Takayuki Morifuji·Masaaki Suzuki

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Abstract

In our previous work, we introduced the notion of a twisted Alexander vanishing (TAV) group, defined as a finite group for which the corresponding twisted Alexander polynomial of a knot vanishes. In this paper, we discuss the orders of TAV groups and construct knots whose twisted Alexander polynomials vanish. Moreover, we show that every faithful irreducible representation of a TAV group causes the twisted Alexander polynomial to be zero.

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Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki. 2026-05-13. Twisted Alexander vanishing groups of knots. https://arxiv.org/abs/2605.13291

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