Cantor systems, piecewise translations and simple amenable groups


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.


Kate Juschenko

Vanderbilt University, Nashville, TN 37240

Current address:

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208 Nicolas Monod

SB - MATHGEOM - EGG, EPFL Station 8, CH-1015 Lausanne, Switzerland