Eilenberg-Mac Lane spectra
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- by H. R. Margolis PDF
- Proc. Amer. Math. Soc. 43 (1974), 409-415 Request permission
Abstract:
Let $K({Z_p})$ be the Eilenberg-Mac Lane spectrum with homotopy ${Z_p}$ and let $A = {H^ \ast }(K({Z_p});{Z_p})$—the $\bmod p$ Steenrod algebra. Let $X$ be a locally finite spectrum. It is proven that \[ [K({Z_p}),X] \to {\operatorname {Hom} _A}({H^ \ast }(X;{Z_p}),A)\] is an isomorphism. It is also proven that there is a unique decomposition $X = ( \oplus K({Z_p})) \oplus Y$ where ${H^ \ast }(Y;{Z_p})$ as an $A$-module has no free summands.References
- J. F. Adams and H. R. Margolis, Modules over the Steenrod algebra, Topology 10 (1971), 271–282. MR 294450, DOI 10.1016/0040-9383(71)90020-6 J. M. Boardman, Stable homotopy theory, Warwick lecture notes series (1965). —, Stable homotopy theory, Chap. II, preprint (1970). H. R. Margolis, Modules over the Steenrod algebra and stable homotopy theory, (to appear).
- John C. Moore and Franklin P. Peterson, Nearly Frobenius algebras, Poincaré algebras and their modules, J. Pure Appl. Algebra 3 (1973), 83–93. MR 335572, DOI 10.1016/0022-4049(73)90007-8 R. M. Vogt, Boardman’s stable homotopy category, Lecture Note Series, no. 21, Aarhus Univ., Aarhus, 1970. MR 43 #1187.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 409-415
- MSC: Primary 55G10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0341488-9
- MathSciNet review: 0341488