Compléments à la démonstration de la conjecture de Baum-Connes pour certains groupes possédant la propriété (T)

✍ Scribed by Vincent Lafforgue

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 490 KB
• Volume: 328
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80122-0

✦ Synopsis

Nous complCtons [3] et nous donnons une preuve purement I(-thCorique de la conjecture de Connes-Kasparov pour les groupes de Lie semi-simples. 0 Acadkmie des ScienceslElsevier, Paris Complements to the proof of the Baum-Connes conjecture for some groups satisfying property (T) We complete [3] and we give a purely K-theoretic proof of the Cannes-Kasparov conjecture .for semi-simple Lie groups. 0 AcadCmie des ScienceslElsevier, Paris Abridged English Version We first sketch the proof of Proposition 4. I of [3]. Let (X, d) b e a weakly bolic weakly geodesic and uniformly locally finite metric space (see [I]) such that for any S > O and any 7' > 0 there exists R > 0 such that for any 1c, y, z, t in X satisfying d(z, y) + a(z,t) 5 7' and d(z:, z) + d(y) t) 2 R, we have d(z, t) + d(y, z) 5 d(z, z) + cZ(y, t) + 2s. Let G be a locally compact group acting continuously properly and isometrically on (X. d). Let s E a;9; and fix 2 E X. We prove that y E KKG(C, C) (constructed by Skandalis and Kasparov in [ 11) has the same image as 1 in KKg%.< (C, C), where &(,y) = cscl(z.@').