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 \([0,1]\).