Twisted Alexander polynomials of a knot for group extensions

Katsumi Ishikawa; Takayuki Morifuji; Masaaki Suzuki

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arXiv · 2605.13288

Twisted Alexander polynomials of a knot for group extensions

Katsumi Ishikawa·Takayuki Morifuji·Masaaki Suzuki

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Abstract

In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated with the regular representation of a finite group. Secondly, we consider twisted Alexander polynomials of a knot for a series of central extensions of a finite group. Moreover, we apply these formulas for twisted Alexander polynomials to the study of twisted Alexander vanishing groups and orders for non-fibered knots.

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Katsumi Ishikawa, Takayuki Morifuji, Masaaki Suzuki. 2026-05-13. Twisted Alexander polynomials of a knot for group extensions. https://arxiv.org/abs/2605.13288

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