The ${\rm SL}(2,\mathbb{C})$-character variety of the Borromean link

TL;DR

This paper computes the irreducible ${ m SL}(2, ext{C})$-character variety of the Borromean link and derives a formula for its twisted Alexander polynomial as a function on this variety.

Contribution

It provides the explicit description of the character variety and a formula for the twisted Alexander polynomial specific to the Borromean link.

Findings

Explicit irreducible ${ m SL}(2, ext{C})$-character variety for the Borromean link

A formula for the twisted Alexander polynomial on the character variety

Enhanced understanding of link invariants in relation to character varieties

Abstract

For the Borromean link, we determine its irreducible ${\rm SL}(2,\mathbb{C})$-character variety, and find a formula for the twisted Alexander polynomial as a function on the character variety.