The coarse Baum–Connes conjecture and groupoids - Texas A&M University (TAMU) Scholar

To every discrete metric space with bounded geometry X we associate a groupoid G(X) for which the coarse assembly map for X is equivalent to the Baum-Connes assembly map for G(X) with coefficients in the C* -algebra L∞ (X, K). We thus obtain a new proof of the fact that if X admits a uniform embedding into Hilbert space, the coarse assembly map is an isomorphism. If furthermore X is a discrete group γ with a translation-invariant metric, we show, using Higson's descent technique, that γ also satisfies the Novikov conjecture. This removes the finiteness condition in (Yu, Invent. Math. 139 (2000) 201-204). © 2002 Elsevier Science Ltd. All rights reserved.

The coarse Baum–Connes conjecture and groupoids Academic Article