The coarse Baum–Connes conjecture and groupoids Academic Article uri icon

abstract

  • 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.

altmetric score

  • 3

author list (cited authors)

  • Skandalis, G., Tu, J. L., & Yu, G.

citation count

  • 69

complete list of authors

  • Skandalis, G||Tu, JL||Yu, G

publication date

  • July 2002