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
However, our theories h G (w ex. 1.
2) an__~dH(X,Y;h for their common limit. I. 2. H(X,Y;h ), F(X,Y;h ) are cohomology theories in each variable X,Y 40 separately, and r : H(X,Y;h ) + h ( X A Y ) is if for some p Xp -or Y p is a Kunneth space. an. isomorphism . F are defined in w pp. 24-5 ). ~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.
O Notes I. Trivially, e @ sTM is a Kunneth space for any h ; and the category of K~nneth spaces is closed under suspensions and wedges. (I know of no case where the distinction between 'left' and 'right' Kunneth spaces etc. makes any difference, so I shall only observe it when it seems that it might). 2. It may be possible to drop finiteness restrictions and deal with completed tensor products (with respect to some topology). These questions may be- come particularly important in the case of To~/B.