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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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