Metabelian SL(n,C) representations of knot groups IV: twisted Alexander polynomials

TL;DR

This paper investigates twisted Alexander polynomials of knots related to metabelian representations, addressing open questions and conjectures to advance understanding of their properties and behaviors.

Contribution

It provides new results on the twisted Alexander polynomial for tensor product representations and resolves several existing conjectures in the field.

Findings

Answer to Wada's question on tensor product twisted Alexander polynomials

Resolution of multiple conjectures by Hirasawa and Murasugi

Enhanced understanding of properties of metabelian SL(n,C) representations

Abstract

In this paper we will study properties of twisted Alexander polynomials of knots corresponding to metabelian representations. In particular we answer a question of Wada about the twisted Alexander polynomial associated to the tensor product of two representations, and we settle several conjectures of Hirasawa and Murasugi.