University of Sydney Algebra Seminar

Richard Garner (Macquarie University)

Friday 1 March, 12-1pm, Place: Carslaw 375

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 $[0,1]$.