A new look at KK-theory
- 1 January 1987
- Vol. 1 (1) , 31-51
- https://doi.org/10.1007/bf00533986
Abstract
We describe the Kasparov group KK(A, B) as the set of homotopy classes of homomorphisms from an algebra qA associated with A into K? B. The algebra qA consists of ‘K-theory differential forms’ over A. Its construction is dual to that of M2(A). The analysis of qA and of its interplay with M2(A) gives the basic results of KK-theory.Keywords
This publication has 4 references indexed in Scilit:
- The Longitudinal Index Theorem for FoliationsPublications of the Research Institute for Mathematical Sciences, 1984
- Some remarks on Kasparov theoryJournal of Functional Analysis, 1984
- K-TheoryPublished by Springer Nature ,1978
- Extensions of C ∗ -algebras and K-HomologyAnnals of Mathematics, 1977