The ${\rm SL}(2,\mathbb{C})$-character variety of the magic $3$-manifold

TL;DR

This paper computes the irreducible ${ m SL}(2, ext{C})$-character variety of the magic 3-manifold and derives formulas for associated twisted Alexander polynomials.

Contribution

It provides the first explicit description of the irreducible ${ m SL}(2, ext{C})$-character variety for the magic 3-manifold and formulates the twisted Alexander polynomial for each representation.

Findings

Explicit irreducible ${ m SL}(2, ext{C})$-character variety obtained.

Formula for twisted Alexander polynomial associated to each ${ m SL}(2, ext{C})$-representation derived.

Abstract

We determine the irreducible ${\rm SL}(2,\mathbb{C})$-character variety of the 3-chain link exterior which is called the `magic $3$-manifold', and deduce a formula for the twisted Alexander polynomial associated to each ${\rm SL}(2,\mathbb{C})$-representation.