The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing s...

BACKGROUND Although advances in early detection and treatment of cancer improve overall population survival, these advances may not benefit all population groups equally and may heighten racial/ethnic differences in survival. METHODS We identified cancer cases in the Surveillance, Epidemiology and End Results program, who were ages > or = 20 years and diagnosed with one invasive cancer in 199...

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this mor...

Topological rigidity is an analogue of the Baum-Connes conjecture, and is motivated by Mostow rigidity and Margulis superrigidity. I will discuss some of the places where this heuristic reasoning fails, and the rigidity shows some cracks – that are rather different than the places where strong forms of the Baum-Connes conjecture fails.

We perform the Batalin-Vilkovisky quantization of Yang–Mills theory on a 2-point space, discussing the formulation of Connes–Lott as well as Connes’ real spectral triple approach. Despite of the model’s apparent simplicity the gauge structure reveals infinite reducibility and the gauge fixing is afflicted with the Gribov problem. 1

We construct a KK-theory for Banach algebras, equivariant with respect to the action of a groupoid. We prove the Baum–Connes conjecture with commutative coefficients for hyperbolic groups and for the Poincaré groupoids of foliations with a compact base and a longitudinal Riemannian metrics with negative sectional curvature. Mots clés : théorie de Kasparov ; conjecture de Baum–Connes ; algèbres ...

For any countable discrete group Γ (without further assumptions on it) we first construct an explicit morphism from the Left-Hand side of Baum-Connes assembly map, Ktop⁎(Γ), to periodic cyclic homology algebra, HP⁎(CΓ). This morphism, called Chern-Baum-Connes allows in particular give a proper and formulation for Chern-Connes pairingKtop⁎(Γ)×HP⁎(CΓ)⟶C. Several theorems are needed formulate map....