The splitting of 𝐵𝑂⟨8⟩∧𝑏𝑜 and 𝑀𝑂⟨8⟩∧𝑏𝑜

Davis, Donald M.

doi:10.1090/S0002-9947-1983-0688969-6

The splitting of $B\textrm {O}\langle 8\rangle \wedge b\textrm {o}$ and $M\textrm {O}\langle 8\rangle \wedge b\textrm {o}$
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by Donald M. Davis

Trans. Amer. Math. Soc. 276 (1983), 671-683

DOI: https://doi.org/10.1090/S0002-9947-1983-0688969-6

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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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