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].