On an intermediate bivariant theory for $C^*$algebras, I
Abstract
We construct a new bivariant theory, that we call $KE$theory, which is intermediate between the $KK$theory of G. G. Kasparov, and the $E$theory of A. Connes and N. Higson. For each pair of separable graded $C^*$algebras $A$ and $B$, acted upon by a locally compact $\sigma$compact group $G$, we define an abelian group $KE_G(A,B)$. We show that there is an associative product $KE_G(A,D) \otimes KE_G(D,B) \to KE_G(A,B)$. Various functoriality properties of the $KE$theory groups and of the product are presented. The new theory has a simpler product than $KK$theory and there are natural transformations $KK_G \to KE_G$ and $KE_G \to E_G$. The complete description of these maps will form the substance of a second paper.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2002
 arXiv:
 arXiv:math/0211160
 Bibcode:
 2002math.....11160D
 Keywords:

 Operator Algebras;
 19K35;
 46L80;
 46L85
 EPrint:
 44 pages