Cantor systems, piecewise translations and simple amenable groups

• 成果类型: Article
• 署名作者: Juschenko, Kate; Monod, Nicolas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.2.7
• 发表日期: 2013
• 页码: 775-787
• 关键词: full groups

摘要

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.