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) |
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Pages (from-to) | 775-787 |
Number of pages | 13 |
Journal | Annals of Mathematics |
Volume | 178 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2013 |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty