Extensions of amenable groups by recurrent groupoids Academic Article

abstract

• 2016, Springer-Verlag Berlin Heidelberg. 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 Grigorchuks 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.

authors

• Nekrashevych, Volodymyr

published proceedings

• INVENTIONES MATHEMATICAE

altmetric score

• 0.25

author list (cited authors)

• Juschenko, K., Nekrashevych, V., & de la Salle, M.

citation count

• 13

publication date

• December 2016

publisher

• Springer Nature  Publisher

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00222-016-0664-6

start page

• 837

end page

• 867

volume

• 206

issue

• 3

URL

• http://dx.doi.org/10.1007/s00222-016-0664-6