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Knots and links from the Thompson groups

Presented by: 
Vaughan Jones Vanderbilt University, University of California, Berkeley, University of Auckland
Date: 
Wednesday 14th June 2017 - 13:00 to 14:00
Venue: 
INI Seminar Room 1
Abstract: 
We will begin with a general procedure for constructing actions ofgroups of fractions of certain categories and give a few examples of this procedure.We then realise the Thompson groups F, T and V as groups of fractions of categories of forestsand obtain many actions of these groups on many spaces. By representing the category of forests on Conway tangles one obtains constructions of knots and links from F and T and we can show that any link can be obtained in this way. Applying a TQFT gives unitary representations on Hilbert spacewhose coefficients are the TQFT link invariants.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons