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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generalized Steenrod-Hopf invariants for stable homotopy theory

Author: Warren M. Krueger
Journal: Proc. Amer. Math. Soc. 39 (1973), 609-615
MSC: Primary 55H15
MathSciNet review: 0385860
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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.

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Keywords: Stable homotopy theory, spectrum, coalgebra, comodule, homology operation, exact couple, canonical injective resolution, extended comodule, unitary spectrum
Article copyright: © Copyright 1973 American Mathematical Society