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

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.

21 pages, 1 figure

References in corpus (6)

• Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants
• Metabelian SL(n,C) representations of knot groups
• Metabelian SL(n,C) representations of knot groups, III: deformations
• Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations
• Metabelian SL(n,C) representations of knot groups II: fixed points
• Twisted Alexander polynomials of 2-bridge knots associated to metabelian representations

Cited by in corpus (3)

• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials
• Deformations of reducible representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$
• Higher dimensional twisted Alexander polynomials for metabelian representations