A universal multicoefficient theorem for the Kasparov groups

A Universal Multi-coefficient Theorem for the Kasparov Groups

that holds in the same generality as the universal coefficient theorem of Rosenberg and Schochet. There are advantages, in some circumstances, to using HomΛ(K(A),K(B)) in place of KK(A,B). These advantages derive from the fact that K(A) can be equipped with order and scale structures similar to those on K0(A). With this additional structure, the “Λ−module” K(A) becomes a powerful invariant of C...

20 02 the Connes - Kasparov Conjecture for Almost Connected Groups

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

On the topology of the Kasparov groups and its applications

In this paper we establish a direct connection between stable approximate unitary equivalence for ∗-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this to...

Mani and shapur a universal faith for e universal kingdom

the local nilpotence theorem for 4-engel groups revisited

the proof of the local nilpotence theorem for 4-engel groups was completed by g. havas and m. vaughan-lee in 2005. the complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. in the process we are also able to make few simplifications and in particular we are able to merge two of the key steps into one.