Cantor systems, piecewise translations and simple amenable groups

Abstract

We provide the first examples of finitely generated simple groups that are amenable (and infinite). To this end, we prove that topological full groups of minimal systems are amenable. This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space. © 2013 Department of Mathematics, Princeton University.