Local 𝐻-maps of classifying spaces

Lance, Timothy

doi:10.1090/S0002-9947-1979-0539915-6

Local $H$-maps of classifying spaces
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by Timothy Lance PDF

Trans. Amer. Math. Soc. 254 (1979), 195-215 Request permission

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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