Uniform Local Amenability implies Property A

Elek, Gabor (2020) Uniform Local Amenability implies Property A. Proceedings of the American Mathematical Society. ISSN 0002-9939 (In Press)

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Abstract

In this short note we answer a query of Brodzki, Niblo, \v{S}pakula, Willett and Wright \cite{ULA} by showing that all bounded degree uniformly locally amenable graphs have Property A. For the second result of the note recall that Kaiser \cite{Kaiser} proved that if $\Gamma$ is a finitely generated group and $\{H_i\}^\infty_{i=1}$ is a Farber sequence of finite index subgroups, then the associated Schreier graph sequence is of Property A if and only if the group is amenable. We show however, that there exist a non-amenable group and a nested sequence of finite index subgroups $\{H_i\}^\infty_{i=1}$ such that $\cap H_i=\{e_\Gamma\}$, and the associated Schreier graph sequence is of Property A.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the American Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
148420
Deposited By:
Deposited On:
22 Oct 2020 12:10
Refereed?:
Yes
Published?:
In Press
Last Modified:
04 Dec 2020 14:55