Vol. 98, No. 2, 1982

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Topological methods for C-algebras. II. Geometry resolutions and the Künneth formula

Claude Schochet

Vol. 98 (1982), No. 2, 443–458

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 Z2-graded Künneth exact sequence

0K(A) K(B) K(A B)
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 surjective and K(F) is free abelian.

Mathematical Subject Classification 2000
Primary: 46M20
Secondary: 46L05, 58G12
Received: 11 November 1980
Published: 1 February 1982
Claude Schochet