# Twisted Alexander polynomials of torus links

## TL;DR

This paper provides explicit formulas for twisted Alexander polynomials of torus links, demonstrating their local constancy on the $SL(2, C)$-character variety and exploring related invariants.

## Contribution

It introduces explicit formulas for twisted Alexander polynomials of torus links and analyzes their behavior on the character variety, extending to higher-dimensional cases.

## Key findings

- Twisted Alexander polynomial formulas are explicitly derived for torus links.
- The polynomial is shown to be locally constant on the $SL(2, C)$-character variety.
- Connections to higher-dimensional twisted Alexander polynomials and Reidemeister torsion are discussed.

## Abstract

In this paper we give an explicit formula for the twisted Alexander polynomial of any torus link and show that it is a locally constant function on the $SL(2, \mathbb C)$-character variety. We also discuss similar things for the higher dimensional twisted Alexander polynomial and the Reidemeister torsion.