Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups E G(A, B) which generalize the E-theory groups of Connes …
For any pair ([italic]A, [italic]B) of [italic]C*-algebras equipped with continuous actions of a locally compact group [italic]G, denote by [italic]KK[italic exponent]G [over] [subscript]* ([italic]A, [italic]B) the equivariant [italic]KK-groups of Kasparov. These groups play a …
Introduction to the Baum-Connes conjecture
The Baum-Connes conjecture is part of A. Connes' non-commutative geometry programme. It can be viewed as a conjectural generalisation of the Atiyah-Singer index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of…
