Twisted Alexander vanishing groups of knots
Geometric Topology
2026-05-14 v1
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.
Keywords
Cite
@article{arxiv.2605.13291,
title = {Twisted Alexander vanishing groups of knots},
author = {Katsumi Ishikawa and Takayuki Morifuji and Masaaki Suzuki},
journal= {arXiv preprint arXiv:2605.13291},
year = {2026}
}
Comments
22 pages, 1 figure. A part of this paper is contained in our unpublished manuscript arXiv:2510.25574. In this paper, we develop it from the viewpoint of TAV groups