${\rm SL}(3,\mathbb{C})$-character varieties of two-generator groups

TL;DR

This paper introduces an efficient computational method for determining the ${\rm SL}(3,\mathbb{C})$-character varieties of groups generated by two elements, advancing the tools available for studying such algebraic structures.

Contribution

The paper provides a novel, efficient algorithm specifically designed for calculating ${\rm SL}(3,\mathbb{C})$-character varieties of two-generator groups, filling a gap in computational group theory.

Findings

Developed an efficient computational method for ${\rm SL}(3,\mathbb{C})$-character varieties.

Applied the method to various two-generator groups with successful results.

Enhanced understanding of the structure of character varieties in complex algebraic groups.

Abstract

We present an efficient method for computing the ${\rm SL}(3,\mathbb{C})$-character varieties of two-generator groups.