Bounded geometry version of property A

2025/06/01 by Manuilov, V.
#FOS: Mathematics #Metric Geometry (math.MG) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2506.00890

Abstract

For uniformly dicrete metric spaces without bounded geometry we suggest a modified version of property A based on metrics of bounded geometry greater than the given metric. We show that this version still implies coarse embeddability in Hilbert spaces, and that some examples of non-property A spaces of unbounded geometry satisfy this version. We also relate this version of property A to our version of uniform Roe algebras for spaces without bounded geometry and introduce an appropriate equivalence relation.

Related

• Two versions of the uniform Roe algebras for spaces without bounded geometry
• Coarse non-amenability and coarse embeddings
• Embeddings of uniform Roe algebras
• Bounded Scale Measure and Property A
• Maximal and reduced Roe algebras of coarsely embeddable spaces