Building weight-free Følner sets for Yu's Property A in coarse geometry
Building weight-free Følner sets for Yu's Property A in coarse geometry
In this note 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.
coarse geometry, Yu’s property A, amenability, uniformly finite homology, Følner sets, Rips complex, flow, naive property A
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Zhang, Jiawen
03e225ff-faf6-4ebc-b719-f8a97bfae8ce
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Zhang, Jiawen
03e225ff-faf6-4ebc-b719-f8a97bfae8ce
Niblo, Graham A., Wright, Nick and Zhang, Jiawen
(2024)
Building weight-free Følner sets for Yu's Property A in coarse geometry.
Algebraic & Geometric Topology.
(In Press)
Abstract
In this note 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.
Text
non-amenability_and_naive_Property_A-AGT-new-title
- Accepted Manuscript
More information
Accepted/In Press date: 28 August 2024
Keywords:
coarse geometry, Yu’s property A, amenability, uniformly finite homology, Følner sets, Rips complex, flow, naive property A
Identifiers
Local EPrints ID: 494301
URI: http://eprints.soton.ac.uk/id/eprint/494301
ISSN: 1472-2747
PURE UUID: 8bd72dde-93c0-485c-9917-cb71540fddfd
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Date deposited: 03 Oct 2024 16:42
Last modified: 04 Oct 2024 01:40
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Author:
Jiawen Zhang
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