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arXiv · 1204.2132

Cantor systems, piecewise translations and simple amenable groups

Kate Juschenko·Nicolas Monod
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Abstract

We provide the first examples of finitely generated simple groups that are amenable (and infinite). 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.

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Kate Juschenko, Nicolas Monod. 2012-04-10. Cantor systems, piecewise translations and simple amenable groups. https://arxiv.org/abs/1204.2132

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