Extensions of amenable groups by recurrent groupoids

By Kate Juschenko, Volodymyr V. Nekrashevych, Mikael de la Salle. 2013

57 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a60f289bc961142fe89d13007dc5065c0211650

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Palindromic subshifts and simple periodic groups of intermediate growth (2016, methodology): “It is interesting to note that the proof of the main result of [JM13], as analyzed in [JNdlS13] and [JMMdlS], is also using a similar idea: trajectories of a random walk on the orbital graph Γζ eventually return back to ζ with probability one.”