Cantor systems, piecewise translations and simple amenable groups

Kate Juschenko*, Nicolas Monod

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)775-787
Number of pages13
JournalAnnals of Mathematics
Volume178
Issue number2
DOIs
StatePublished - Sep 2013

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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