Cantor systems, piecewise translations and simple amenable groups

Kate Juschenko; Nicolas Monod

doi:10.4007/annals.2013.178.2.7

Cantor systems, piecewise translations and simple amenable groups

Kate Juschenko^*, Nicolas Monod

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

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.

Original language	English (US)
Pages (from-to)	775-787
Number of pages	13
Journal	Annals of Mathematics
Volume	178
Issue number	2
DOIs	https://doi.org/10.4007/annals.2013.178.2.7
State	Published - Sep 2013

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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