Algebra Seminar: Garner -- V, J--T, F and L

Richard Garner (Macquarie University)

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

Title: V, J--T, F and L

Abstract: 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 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].