$B_3$ block representations of dimension 6 and braid reversions

TL;DR

This paper introduces a new family of six-dimensional representations of the braid group B_3, which can be used to distinguish certain knots and their reversibility, advancing knot detection methods.

Contribution

The authors construct novel six-dimensional block representations of B_3 and demonstrate their application in detecting braid reversibility of complex knots.

Findings

Some representations detect braid reversibility of known knots.

Representations can distinguish knots with 9 and 10 crossings.

New tools for knot analysis using braid group representations.

Abstract

We construct a family of six dimensional block representations of the braid group $B_3$ on three strings. We show that some of these representations can be used to detect braid vertibility of some known knots and others of 9 and 10 crossings.