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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
Classifying Space for Proper Actions and K-Theory of Group C*-algebras
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
E-theory and KK-theory for groups which act properly and isometrically on Hilbert space
A good deal of research in C∗-algebra K -theory in recent years has been devoted to the Baum-Connes conjecture , which proposes a formula for the K -theory of group C∗-algebras that blends group… Expand
Counterexamples to the Baum—Connes conjecture
Abstract. ((Without Abstract)).
Equivariant E-Theory for C*-Algebras
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
On the Equivalence of Geometric and Analytic K-Homology
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
Operator -theory for groups which act properly and isometrically on Hilbert space
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
C*-Algebras and Controlled Topology
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