Topological methods for c*-algebras II: Geometric resolutions and the Kunneth formula

Abstract

Let A and B be C*-algebras with A in the smallest subcategory of the category of separable nuclear C*-algebras which contains the separable Type I algebras and is closed under the operations of taking ideals, quotients, extensions, inductive limits, stable isomorphism, and crossed products by Z and by R. Then there is a natural Z/2-graded Knneth exact sequence. Our proof uses the technique of geometric realization. The key fact is that given a unital C*-algebra B, there is a commutative C*-algebra F and an inclusion F→ B⊗ K such that the induced map K*(F) → K*(B) is sur jective and K*(F) is free abelian. © 1982, University of California, Berkeley. All Rights Reserved.