Some notes on property A

Abstract

We provide an expository account of Guoliang Yu's property A. The piece starts from the basic definitions, and goes on to discuss closure properties of the class of property A spaces (and groups) and the relationship of property A to coarse embeddability problems, operator theory, and amenability. It finishes with some examples of non-property A spaces. We also include an annotated bibliography covering much of the related literature.

References in corpus (1)

• On generalized amenability

Cited by in corpus (17)

• Uniform Roe algebras of uniformly locally finite metric spaces are rigid
• Limit operators techniques on general metric measure spaces of bounded geometry
• Property A and asymptotic dimension
• Dynamical complexity and controlled operator K-theory
• Sofic boundaries of groups and coarse geometry of sofic approximations
• The type semigroup, comparison and almost finiteness for ample groupoids
• The uniform Roe algebra of an inverse semigroup
• Quasi-local Algebras and Asymptotic Expanders
• A Markovian and Roe-algebraic approach to asymptotic expansion in measure
• On equivariant asymptotic dimension
• Extreme cases of limit operator theory on metric spaces
• K-theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations
• Property {A} and duality in linear programming
• Remarks on strong embeddability for discrete metric spaces and groups
• Asymptotic dimension of coarse spaces via maps to simplicial complexes
• On Rigidity of Roe algebras
• Dynamic asymptotic dimension and Matui's HK conjecture