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Transactions of the American Mathematical Society

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



The splitting of $ B{\rm O}\langle 8\rangle \wedge b{\rm o}$ and $ M{\rm O}\langle 8\rangle \wedge b{\rm o}$

Author: Donald M. Davis
Journal: Trans. Amer. Math. Soc. 276 (1983), 671-683
MSC: Primary 55R12; Secondary 55R45
MathSciNet review: 688969
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Abstract: Let $ BO\left\langle 8 \right\rangle $ denote the classifying space for vector bundles trivial on the $ 7$-skeleton, and $ MO\left\langle 8 \right\rangle $ the associated Thom spectrum. It is proved that, localized at $ 2$, $ BO\left\langle 8 \right\rangle \wedge \,bo$ and $ MO\left\langle 8 \right\rangle \wedge \,bo$ split as a wedge of familiar spectra closely related to $ bo$, where $ bo$ is the spectrum for connective $ KO$-theory.

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Keywords: Splittings of spectra, connective $ K$-theory, Brown-Gitler spectra, Thom spectra
Article copyright: © Copyright 1983 American Mathematical Society