Cantor systems, piecewise translations and simple amenable groups

• Autores: Kate Juschenko, Nicolas Monod
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 178, Nº 2, 2013, págs. 775-787
• Idioma: inglés
• DOI: 10.4007/annals.2013.178.2.7
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• Resumen

  • 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