Equivariant Kasparov theory and generalized homomorphisms

By R. Meyer. 2000

65 citations recorded by the source corpus.

Let G be a locally compact group. We describe elements of KK^G (A,B) by equivariant homomorphisms, following Cuntz's treatment in the non-equivariant case. This yields another proof for the universal property of KK^G: It is the universal split exact stable homotopy functor. To describe a Kasparov triple (E, phi, F) by an equivariant homomorphism, we have to arrange for the Fredholm operator F to be equivariant. This can be done if A is of the form K(L^2G) otimes A' and more generally if the group action on A is proper in the sense of Rieffel and Exel.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bbc0c77a927efc51cfd2c280b27fd917b32ecca9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. R. Nest
2. M. Joachim
3. R. Meyer

In Geometry and Topology

1. R. Nest
2. M. Joachim
3. R. Meyer
4. S. Schwede
5. Alain Connes
6. Christian Voigt
7. Matilde Marcolli
8. C. Consani

In Mathematical Physics

1. R. Nest
2. M. Joachim
3. R. Meyer
4. S. Schwede
5. Alain Connes
6. Christian Voigt
7. Matilde Marcolli
8. S. Echterhoff

Citations in the corpus

• The Baum-Connes Conjecture via Localization of Categories (2003, methodology): “The universal C∗-algebra qsA is defined in [34].”
• K-homology of C*-categories and symmetric spectra representing K-homology (2003, background): “The relevant statements can be found in [2],[11] and [15].”