~F~) ' ' ' is the inclusion. The rank of W is equal to rank ~k(N F'' F'i ) / 2 and "ITk(N' F~' F'i ) / Ji.

N span a d i r e c t summand in II-k(NF,FI) and vanish in ITk(NF,Fo) while ~ 1 . . ' ~ n span a direct summand in ITk(NF,Fo) and vanish in II'k(NF,F1). i Let W C'ITk(N F' ) be the subspace generated by ~ 1 + ~C-I. . . ~n + ~ ' ~ I +#1 . . . n-dimensional d ire ct summand in ~ k ( N ' F ' , F'i ) for i = 0 and 1 and for x,y E W the intersection number x o y vanishes. d. 4. Then the linking form L(~N F) on Tor H2k_I(QNF) vanishes in W(~/Z).

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