Wednesday 28 October from 11:00–12:00 in Carslaw 535A

Commutators in groups of piecewise projective homeomorpisms

Lawrence Reeves (Melbourne)

Abstract

The Lodha-Moore groups are finitely presented counterexamples to the von Neumann-Day conjecture.  They appear as subgroups of a group of piecewise projective maps constructed by Monod. Elements in these groups can be represented as pairs of binary trees, in a similar way to elements of Thompson's group F. We study their commutators and second commutators, showing some of them are simple. This is joint work with Jose Burillo and Yash Lodha.