Split Injectivity of the Baum-Connes Assembly Map

Split Injectivity of the Baum-connes Assembly Map

In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the Baum-Connes map is a split injection for groups satisfying certain geometric conditions.

The Baum - Connes Assembly Map and the Generalized Bass

Towards the Baum-Connes’ Analytical Assembly Map for the Actions of Discrete Quantum Groups

Given an action of a discrete quantum group (in the sense of Van Daele, Kustermans and Effros-Ruan) A on a C-algebra C, satisfying some regularity assumptions resembling the proper Γ-compact action for a classical discrete group Γ on some space, we are able to construct canonical maps μ r (μ respectively) (i = 0, 1 ) from the Aequivariant K-homology groups KK i (C, C| ) to the K-theory groups K...

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...

Some 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...