论文信息 - The coarse Baum – Connes conjecture and groupoids

The coarse Baum – Connes conjecture and groupoids

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 coe2cients in the C∗-algebra ‘∞(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 with a translation-invariant metric, we show, using Higson’s descent technique, that also satis8es the Novikov conjecture. This removes the 8niteness condition in (Yu, Invent. Math. 139 (2000) 201–204). ? 2002 Elsevier Science Ltd. All rights reserved. MSC: 46L80; 58J22; 22A22; 19K56; 46L85

G. Skandalisa | J. Tua | G. Yub

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