The Homflypt polynomial and the oriented Thompson group. (English) Zbl 1397.57022

Aiello, Valeriano; Conti, Roberto; Jones, Vaughan F. R.

Quantum Topol. 9, No. 3, 461-472 (2018).

Summary: 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 \(\vec F\).

MSC:

57M27	Invariants of knots and \(3\)-manifolds (MSC2010)
20F65	Geometric group theory
43A35	Positive definite functions on groups, semigroups, etc.

Keywords:

unitary representations; positive definite functions; Thompson group \(F\); binary trees; category of forests; group of fractions; HOMFLYPT polynomial; tangles; knots; oriented link invariants; TQFT; subfactors; planar algebras; CFT