Tracefree ${\rm SL}(2,\mathbb{C})$-representations of Montesinos links

TL;DR

This paper classifies tracefree ${ m SL}(2,bC)$-representations of Montesinos links by determining their conjugacy classes, contributing to the understanding of link group representations in complex special linear groups.

Contribution

It provides a complete classification of tracefree ${ m SL}(2,bC)$-representations specifically for Montesinos links, a class of links in knot theory.

Findings

Conjugacy classes of tracefree representations are explicitly determined for Montesinos links.

The classification advances understanding of link group representations in complex Lie groups.

Results may impact studies of link invariants and 3-manifold topology.

Abstract

Given a link $L$, a representation $\pi_1(S^{3}-L)\to {\rm SL}(2,\mathbb{C})$ is {\it tracefree} if the image of each meridian has trace zero. We determine the conjugacy classes of tracefree representations when $L$ is a Montesinos link.