Building weight-free Følner sets for Yu’s property A in coarse geometry

Niblo, Graham A; Wright, Nick; Zhang, Jiawen

doi:10.2140/agt.2025.25.3133

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ISSN (electronic): 1472-2739

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Building weight-free F\o{}lner sets for Yu's property A in coarse geometry

Graham A Niblo, Nick Wright and Jiawen Zhang

Algebraic & Geometric Topology 25 (2025) 3133–3144

DOI: 10.2140/agt.2025.25.3133

Abstract

We study the natural question of when the generalised Følner sets exhibiting property A can be chosen to be subsets of the space itself. We show that for many property-A spaces $X$ , this is indeed possible. Specifically this holds for all discrete bounded geometry metric spaces which coarsely have all components unbounded, for all countable discrete groups, and for all box spaces.

Keywords

coarse geometry, Yu's property A, amenability, uniformly finite homology, Følner sets, Rips complex, flow, naive property A

Mathematical Subject Classification

Primary: 51F30

References

Publication

Received: 10 May 2024

Revised: 16 July 2024

Accepted: 27 August 2024

Published: 17 September 2025

Authors

Graham A Niblo
School of Mathematical Sciences University of Southampton Southampton United Kingdom

Nick Wright
School of Mathematical Sciences University of Southampton Southampton United Kingdom

Jiawen Zhang
School of Mathematical Sciences, Fudan University Shanghai, China

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Volume 25, issue 5 (2025)