# Richard Garner (Macquarie University)

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

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 $$X \to X\times X$$. The first part of this talk explains how these two perspectives on $$V$$ can be unified via sheaf theory, making using of 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 via sheaf theory, making use of some apparently novel results involving a curiously augmented version of $$[0,1]$$.