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Uniform Local Amenability implies Property A

Research output: Contribution to journalJournal articlepeer-review

Forthcoming
<mark>Journal publication date</mark>21/10/2020
<mark>Journal</mark>Proceedings of the American Mathematical Society
Number of pages6
Publication StatusAccepted/In press
<mark>Original language</mark>English

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.