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