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The oriented Thompson group, oriented links, and polynomial link invariants

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OAS - Operator algebras: subfactors and their applications

Recently, Vaughan Jones discovered an unexpected connection between the Thompson groups and knots.  Among other things, he showed that any oriented link can be obtained as the “closure” of elements of the oriented Thompson group $\vec{F}$. By using this procedure we show that certain specializations of some link invariants, notably the Homfly polynomial, are functions of positive type on $\vec{F}$ (up to a renormalization).  As for other specializations, we also show that the corresponding functions are not even bounded (in particular, they are not of positive type). This talk is based on a joint work with Roberto Conti (Sapienza Università di Roma) and Vaughan Jones (Vanderbilt University).



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