Uniform local amenability implies Property A

DOI10.1090/proc/15387zbMath1473.46034arXiv1912.00806OpenAlexW3106449734MaRDI QIDQ4985390

Gábor Elek

Publication date: 23 April 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.00806

zbMATH Keywords

amenabilityproperty~ASchreier graph sequence

Mathematics Subject Classification ID

Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Metric geometry (51F99) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

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Cites Work

• Uniform local amenability
• Sublinear separators, fragility and subexponential expansion
• \(L^{2}\)-spectral invariants and convergent sequences of finite graphs
• Random walk in random groups.
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• The combinatoral cost
• Property A and the operator norm localization property for discrete metric spaces
• Hyperfinite actions on countable sets and probability measure spaces
• Combinatorial cost: A coarse setting