Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Local $ H$-maps of classifying spaces

Author: Timothy Lance
Journal: Trans. Amer. Math. Soc. 254 (1979), 195-215
MSC: Primary 55R35; Secondary 55P45, 55P60
MathSciNet review: 539915
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Abstract: Let BU denote the localization at an odd prime p of the classifying space for stable complex bundles, and let $ f:BU \to BU$ be an H-map with fiber F. In this paper the Hopf algebra $ {H^{\ast}}(F,\textbf{Z}/P)$ is computed for any such f. For certain H-maps f of geometric interest the p-local cohomology of F is given by means of the Bockstein spectral sequence. A direct description of $ {H^ {\ast} }(F,{{\textbf{Z}}_{(P)}})$ is also given for an important special case. Applications to the classifying spaces of surgery will appear later.

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Keywords: Localization, H-map, torsion product, cohomology
Article copyright: © Copyright 1979 American Mathematical Society