noncommutative topology, noncommutative geometry
noncommutative stable homotopy theory
genus, orientation in generalized cohomology
The analytic assembly map is a natural morphism from -equivariant topological K-theory to the operator K-theory of a corresponding crossed product C*-algebra.
More generally in equivariant KK-theory this is called the Kasparov descent map and is of the form
where on the left we have -equivariant KK-theory and on the right ordinary KK-theory of crossed product C*-algebras (which by the discussion there are models for the groupoid convolution algebras of -action groupoids).
(recalled as Blackadar, theorem 20.6.2)
The Baum-Connes conjecture states that under some conditions the analytic assembly map is in fact an isomorphism. The Novikov conjecture makes statements about it being an injection. The Green-Julg theorem states that under some (milder) conditions the Kasparov desent map is an isomorphism.
The construction goes back to
An introduction is in
A textbook account is in
See also
Last revised on July 10, 2013 at 01:06:11. See the history of this page for a list of all contributions to it.