Abstract
Vaughan Jones, in his late years, motivated by an attempt to develop new conformal eld theory, obtained unitary representations of Thompson’s groups F and T and these results further stimulated researches on Jones construction, from both the aspect of pure maths and mathematical physics. As one of the consequences, Jones found a rather concrete way of constructing knots and links from Thompson’s group F as an analogue of results on braid groups. Aiello and Baader extended these results to the positive oriented Thompson’s group !F which is isomorphic to Higman (Brown-) Thompson group F3: In this talk, I would like to present a sequence of computational results on certain sequences of knots and links constructed from certain sequences of words in F and we also provide a way of estimating the number of crossings from some group theoretic property.
History
We talked about the history of the Thompson group.