A short proof of the James periodicity of 𝜋_{𝑘+𝑝}(𝑉_{𝑘+𝑚,𝑚})

Mahowald, Mark

doi:10.1090/S0002-9939-1965-0177411-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A short proof of the James periodicity of $\pi _{k+p}(V_{k+m,m})$
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by Mark Mahowald

Proc. Amer. Math. Soc. 16 (1965), 512

DOI: https://doi.org/10.1090/S0002-9939-1965-0177411-4

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References

J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632. MR 139178, DOI 10.2307/1970213
I. M. James, Cross-sections of Stiefel manifolds, Proc. London Math. Soc. (3) 8 (1958), 536–547. MR 100840, DOI 10.1112/plms/s3-8.4.536
J. H. C. Whitehead, On the groups $\pi _r(V_{n,m})$ and sphere-bundles, Proc. London Math. Soc. (2) 48 (1944), 243–291. MR 12226, DOI 10.1112/plms/s2-48.1.243