Twisted Alexander polynomials of a knot for group extensions
arXiv:2605.13288
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 formula for the twisted Alexander polynomial of a knot in the -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.
13 pages. A part of this paper is contained in our unpublished manuscripts arXiv:2510.25574, arXiv:2311.15484. In this paper, we develop it from the viewpoint of the formulation of twisted Alexander polynomials of a knot for group extensions