noncommutative topology, noncommutative geometry
noncommutative stable homotopy theory
genus, orientation in generalized cohomology
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
(geometry Isbell duality algebra)
The equivariant cohomology version of KK-theory.
Let be a locally compact topological group.
is the category…
(Blackadar, section 20.2) The composition is in (Blackadar, theorem 20.3.1) .
The KK-theoretic representation ring of is the ring
The Green-Julg theorem:
(Green-Julg theorem)
Let be a topological group acting on a C*-algebra .
If is a compact topological group then the descent map
is an isomorphism, identifying the equivariant operator K-theory of with the ordinary operator K-theory of the crossed product C*-algebra .
if is a discrete group then the descent map
is an isomorphism, identifying the equivariant K-homology of with the ordinary K-homology of the crossed product C*-algebra .
If is a compact topological group, then the KK-theoretic representation ring, def. coincides with the ordinary representation ring of .
Section 20 of
Last revised on July 18, 2013 at 13:13:22. See the history of this page for a list of all contributions to it.