The Homflypt polynomial and the oriented Thompson group

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 $\vec{F}$.

To appear in Quantum Topology

Cited by in corpus (11)

• On the Alexander Theorem for the oriented Thompson group $\vec{F}$
• Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras
• The Jones polynomial and functions of positive type on the oriented Jones-Thompson groups $\vec{F}$ and $\vec{T}$
• Arborescence of positive Thompson links
• On the $3$-colorable subgroup $\mathcal{F}$ and maximal subgroups of Thompson's group $F$
• On the oriented Thompson subgroup ${\vec{F}}_3$ and its relatives in higher Brown-Thompson groups
• Positive oriented Thompson links
• An introduction to Thompson knot theory and to Jones subgroups
• On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots
• Remarks on some maximal subgroups of $F$ and on the $\vec{F}$-index of knots
• The planar $3$-colorable subgroup $\mathcal{E}$ of Thompson's group $F$ and its even part