The symmetric slice of ${\rm SL}(3,\mathbb{C})$-character variety of the Whitehead link

TL;DR

This paper describes a Zariski open subset of the ${ m SL}(3, ext{C})$-character variety associated with the Whitehead link, providing insights into its algebraic structure.

Contribution

It offers a detailed description of a specific subset of the ${ m SL}(3, ext{C})$-character variety for the Whitehead link, advancing understanding of its geometric properties.

Findings

Identification of a Zariski open subset of the character variety.

Explicit algebraic description of the subset.

Enhanced understanding of the Whitehead link's character variety.

Abstract

We give a nice description for a Zariski open subset of the ${\rm SL}(3,\mathbb{C})$-character variety of the Whitehead link.