Extensions of amenable groups by recurrent groupoids

• 成果类型: Article
• 署名作者: Juschenko, Kate; Nekrashevych, Volodymyr; de la Salle, Mikael
• 署名单位: Northwestern University; Texas A&M University System; Texas A&M University College Station; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0664-6
• 发表日期: 2016
• 页码: 837-867
• 关键词: hyperbolic polynomial diffeomorphisms; inductive limits; amenability; GROWTH; PRODUCTS; Automata; sets

摘要

We show that the amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, the amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk's group, Basilica group, group associated to Fibonacci tiling, the topological full groups of Cantor minimal systems, groups acting on rooted trees by bounded automorphisms, groups generated by finite automata of linear activity growth, and groups naturally appearing in holomorphic dynamics.