Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used… Expand

We announce a reformulation of the conjecture in [8,9,10]. The advantage of the new version is that it is simpler and applies more generally than the earlier statement. A key point is to use the… Expand

A good deal of research in C∗-algebra K -theory in recent years has been devoted to the Baum-Connes conjecture [3], which proposes a formula for the K -theory of group C∗-algebras that blends group… Expand

Introduction Asymptotic morphisms The homotopy category of asymptotic morphisms Functors on the homotopy category Tensor products and descent $C^\ast$-algebra extensions $E$-theory Cohomological… Expand

We give a proof that the geometric K-homology theory for finite CWcomplexes defined by Baum and Douglas is isomorphic to Kasparov’s Khomology. The proof is a simplification of more elaborate… Expand

Let G be a countable discrete group which acts isometrically and metrically properly on an infinite-dimensional Euclidean space. We calculate the K-theory groups of the C∗-algebras C∗ max(G) and C∗… Expand

This paper is an attempt to explain some aspects of the relationship between the K-theory of C-algebras, on the one hand, and the categories of modules that have been developed to systematize the… Expand