Higher dimensional twisted Alexander polynomials for metabelian representations

TL;DR

This paper investigates the asymptotic properties of twisted Alexander polynomials derived from metabelian representations of knot groups, providing limits of leading coefficients and explicit calculations for genus one two-bridge knots.

Contribution

It introduces a new analysis of the asymptotic behavior of twisted Alexander polynomials for SL(n,C) representations induced from metabelian SL(2,C) representations, including explicit computations.

Findings

Limits of leading coefficients in asymptotics are established.

Explicit computations for genus one two-bridge knots are provided.

Connections between twisted Alexander polynomials and Reidemeister torsion are explored.

Abstract

We study the asymptotic behavior of the twisted Alexander polynomial for the sequence of SL(n ,C)-representations induced from an irreducible metabelian SL(2, C)-representation of a knot group. We give the limits of the leading coefficients in the asymptotics of the twisted Alexander polynomial and related Reidemeister torsion. The concrete computations for all genus one two-bridge knots are also presented.