Singularities of the representation variety of the braid group on 3 strands

TL;DR

This paper investigates the singular points of the representation variety of the 3-strand braid group, identifying which semisimple representations correspond to smooth points in this algebraic structure.

Contribution

It provides a detailed analysis of the singularities in the representation variety of B_3 and characterizes smooth points among semisimple representations.

Findings

Identified the smooth points in the representation variety of B_3.

Characterized the singularities associated with non-semisimple representations.

Enhanced understanding of the geometric structure of the B_3 representation variety.

Abstract

The singularities of the representation variety of $B_3$ are studied, where $B_3$ is the knot group on 3 strands. Specifically, we determine which semisimple representations are smooth points of this variety.