A new look at KK-theory
We describe the Kasparov group KK(A,B) as the set of homotopy classes of homomorphisms from an algebra qA associated with A into \({\mathcal K}\otimes B\). The algebra qA consists of `K-theory differential forms' over A. Its construction is dual to that of \(M_ 2(A)\). The analysis of qA and of its interplay with \(M_ 2(A)\) gives the basic results of KK-theory.
scientific article; zbMATH DE number 4036732