By Luke H. Hodgkin, Victor P. Snaith
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Extra info for Topics in K-Theory: The Equivariant Kanneth Theorem in K-Theory. Dyer-Lashof Operations in K-Theory
4. I. Tor~ r (r § h (X A and the identifications Y). I. ~, are natural in X,Y. 1. Let X, be a ~rojective : EI(X,;h in the case that interests us. @o complex, ) @ EI(Y,;h h Y, ~ % complex. Then the pairing ) + EI(X . ;h ) is an isomorphism. Proof If X. is projective, SmXp/X_+ip = SZp is a Kunneth space for all p. 2. < : h (smx /X +l ) @ P P h is an isomorphism. ;h ), au@mented by c, e" over ~*(X), in w D. ;h ~*(Y) respectively; and the discussion which precedes it they are actually resolutions.
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Ii. Eilenberg, and R. Lashof, 12. 13. E. Dyer, L. Hodgkin, 14. M. James, 15. S. MacLane, 15a. 16. J. Milnor, 17. The K-theory of Eilenberg-MacLane complexes, To o _ ~ 7 (1968), 317-329. Characters and cohomology of finite groups, Publ. Math. I H E S 9 (1961), 23-64. Vector bundles and the Kunneth formula, ToDolo~ i (1962), 245-248. K-theory, Benjamin, 1967. On H-spaces and infinite loop spaces. Category Theory, Homology Theory and their Applications III, Lecture Note~ in Mathematics no. 99, Springer, 1969.