The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space

By G. Yu. 2000

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Uniform Embeddings into Hilbert Space and a Question of Gromov (2002, background): “A positive answer to this question would imply the Novikov conjecture on homotopy invariance of higher signatures and Gromov’s conjecture that a uniformly contractible Riemannian manifold can not have uniformly positive scalar curvature [ 17 ].”
The asymptotic dimension of a curve graph is finite (2005, background): “In [ 48 ], Yu defines a property of discrete metric spaces called “property A” guaranteeing the existence of a large-scale (or uniform) embedding into Hilbert space.”
Bivariant K-theory and the Novikov conjecture (2000, methodology): “In a preliminary section of a recent paper [ Y2 ], Guoliang Yu introduced a property of discrete metric spaces which guarantees the existence of a uniform embedding into Hilbert space.”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, methodology): “Property A for metric spaces was introduced by Yu [99] in the work on the Baum-Connes conjecture.”