Multiplicative structures and the twisted Baum-Connes assembly map

The Baum - Connes Assembly Map and the Generalized Bass

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.

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...

Deformation 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...

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...