## J--T, V, L and F

### Richard Garner – 6 February 2019

Thompson's group V is a group of certain self-homeomorphisms of Cantor space. It also admits a combinatorial description, due to Higman, in terms of "Jonsson--Tarski algebras"---sets endowed with a bijection X --> XxX. The first part of this talk explains how these two perspectives on V can be unified by using sheaf theory together with some results of Peter Freyd.

Thompson's group F is a group of certain self-homeomorphisms of the unit interval [0,1]. It also admits a combinatorial description in terms of a generalised notion of Jonsson--Tarski algebra due to Tom Leinster. The second part of this talk explains how these two perspectives on F can be unified by using sheaf theory together with some apparently novel results involving a curiously fattened version of [0,1].

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