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- W1976759211 abstract "In his paper On the groups J(X). IV, Adams suggested that one might try to continue his d and e invariants to a sequence of higher homotopy invariants, each defined upon the vanishing of its predecessors and each taking its value in a certain Ext group. Recently he pointed out the efficacy of relocating his d and e invariants in Ext groups formed over a certain abelian category of comodules. It is the purpose of this note to carry out the program suggested above in a setting of the sort just mentioned. More specifically, for each homology theory which is representable by a comutative ring spectrum and whose ring of cooperations is flat over the coefficient ring, a sequence of higher homotopy invariants is constructed whose first term is Adams' e invariant for this theory. 1. Notation and statement of results. In this section some notation is fixed and the main results of this note are given. Their proofs are deferred until ?3. All spectra and maps considered here are assumed to reside in Boardman's stable category. From now on, E shall denote a commutative ring spectrum with unit i: SO-*E. It shall be further assumed that E*(E) is flat as a left E*(SO) module. Then E*(E) is a Hopf algebra over which E*(X) is a left comodule for any spectrum X. All Hom and Ext groups found here are formed relative to the abelian category of left E*(E) comodules. Letf: X-+ Y be a map whose domain satisfies the isomorphism condition: for any spectrum W, the correspondence [X, E A W]* -? Hom*E*(E)(E*(X), E*(E A W)), given by [g]-*g*, is an isomorphism. This condition obtains, for example, if X satisfies the hypotheses of Proposition 17 of [2]. Received by the editors November 27, 1972. AMS (MOS) subject classifications (1970). Primary 55E25; Secondary 55E45, 55G20." @default.
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- W1976759211 date "1973-03-01" @default.
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- W1976759211 title "Generalized Steenrod-Hopf invariants for stable homotopy theory" @default.
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