منابع مشابه
Banach KK-theory and the Baum-Connes Conjecture
The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group C∗-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups. 2000 Mathematics Subject Classification: 19K...
متن کاملThe Baum-connes Conjecture for Hyperbolic Groups
The Baum-Connes conjecture states that, for a discrete group G, the K-homology groups of the classifying space for proper G-action is isomorphic to the K-groups of the reduced group C-algebra of G [3, 2]. A positive answer to the Baum-Connes conjecture would provide a complete solution to the problem of computing higher indices of elliptic operators on compact manifolds. The rational injectivit...
متن کاملSome Remarks Concerning the Baum-Connes Conjecture
P. Baum and A. Connes have made a deep conjecture about the calculation of the K-theory of certain types of C∗-algebras [1, 2]. In particular, for a discrete group Γ they have conjectured the calculation of K∗(C r (Γ)), the Ktheory of the reduced C∗-algebra of Γ. So far, there is quite little evidence for this conjecture. For example, there is not a single property T group for which it is known...
متن کاملDeformation Quantization and the Baum–Connes Conjecture
Alternative titles of this paper would have been “Index theory without index” or “The Baum–Connes conjecture without Baum.” In 1989, Rieffel introduced an analytic version of deformation quantization based on the use of continuous fields ofC∗-algebras. We review how a wide variety of examples of such quantizations can be understood on the basis of a single lemma involving amenable groupoids. Th...
متن کاملOn the Baum–connes Conjecture in the Real Case
Let be a countable discrete group. We prove that if the usual Baum–Connes conjecture is valid for , then the real form of Baum–Connes is also valid for . This is relevant to proving that Baum–Connes implies the stable Gromov–Lawson–Rosenberg conjecture about Riemannian metrics of positive scalar curvature. 0. Introduction The classical Baum–Connes conjecture (for a given discrete countable grou...
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ژورنال
عنوان ژورنال: Journal of K-Theory
سال: 2010
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is010003012jkt114