Uniform local amenability implies Property A,Proceedings of the American Mathematical Society

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Uniform local amenability implies Property A
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-18 , DOI: 10.1090/proc/15387
Gábor Elek

Abstract:In this short note we answer a query of Brodzki, Niblo, Špakula, Willett and Wright [J. Noncommut. Geom. 7 (2013), pp. 583-603] by showing that all bounded degree uniformly locally amenable graphs have Property A. For the second result of the note recall that Kaiser [Trans. Amer. Math. Soc. 372 (2019), pp. 2855-2874] 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.

中文翻译：

统一的当地舒适度意味着物业A

摘要：在此简短说明中，我们回答了对Brodzki，Niblo，Špakula，Willett和Wright的查询[J. 非通勤。几何 7（2013），第583-603页]，表明所有有界度一致局部可适应图都具有属性A。阿米尔。数学。Soc。372（2019），第2855-2874页]证明，如果 $\伽玛$ 是一个有限生成的组，并且是有限索引子组的Farber序列，则且仅当该组是可接受的时，关联的Schreier图序列才具有属性A。但是，我们表明，存在一个不可满足的组和一个有限索引子组的嵌套序列，使得，并且关联的Schreier图序列具有属性A。 $\ {H_i \} ^ \ infty _ {i = 1}$ $\ {H_i \} ^ \ infty _ {i = 1}$ $\ cap H_i = \ {e_ \ Gamma \}$

更新日期：2021-04-22

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