The Homflypt polynomial and the oriented Thompson group

TL;DR

This paper demonstrates how to derive unitary representations of the oriented Thompson group using oriented link invariants, specifically showing that the HOMFLYPT polynomial yields a positive definite function on the group.

Contribution

It introduces a method to construct unitary representations of the oriented Thompson group from link invariants, highlighting the HOMFLYPT polynomial's role.

Findings

HOMFLYPT polynomial defines a positive definite function on .

Construction of unitary representations from link invariants.

Connection between knot theory and group representations.

Abstract

We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of $\vec{F}$.