The Baum-Connes conjecture for hyperbolic groups
نویسندگان
چکیده
منابع مشابه
The 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 کاملThe Haagerup property, Property (T) and the Baum-Connes conjecture for locally compact Kac-Moody groups
We indicate which symmetrizable locally compact affine or hyperbolic Kac-Moody groups satisfy Kazhdan’s Property (T), and those that satisfy its strong negation, the Haagerup property. This reveals a new class of hyperbolic Kac-Moody groups satisfying the Haagerup property, namely symmetrizable locally compact Kac-Moody groups of rank 2 or of rank 3 noncompact hyperbolic type. These groups thus...
متن کاملA Complete Formulation of Baum-Connes’ Conjecture for the Action of Discrete Quantum Groups
We formulate a version of Baum-Connes’ conjecture for a discrete quantum group, building on our earlier work ([9]). Given such a quantum group A, we construct a directed family {EF} of C -algebras (F varying over some suitable index set), borrowing the ideas of [5], such that there is a natural action of A on each EF satisfying the assumptions of [9], which makes it possible to define the “anal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2002
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220200214