Colored HOMFLY polynomials that distinguish mutant knots

TL;DR

This paper demonstrates how colored HOMFLY polynomials, derived from braiding operations on conformal blocks, can distinguish mutant knots, exemplified by explicitly differentiating the Kinoshita-Terasaka and Conway knots.

Contribution

It introduces a method using braiding operations on WZNW conformal blocks to compute colored HOMFLY polynomials that can detect knot mutations.

Findings

Colored HOMFLY polynomials can distinguish mutant knots.

Explicit evaluation of (2,1)-colored HOMFLY polynomials differentiates the Kinoshita-Terasaka and Conway knots.

Method provides a new tool for knot mutation detection.

Abstract

We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.