The Borsuk-Ulam theorem for a 𝑍_{𝑞}-map from a 𝑍_{𝑞}-space to 𝑆²ⁿ⁺¹

Kobayashi, Teiichi

doi:10.1090/S0002-9939-1986-0845994-8

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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The Borsuk-Ulam theorem for a $Z_ q$-map from a $Z_ q$-space to $S^ {2n+1}$
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by Teiichi Kobayashi

Proc. Amer. Math. Soc. 97 (1986), 714-716

DOI: https://doi.org/10.1090/S0002-9939-1986-0845994-8

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Abstract:

J. W. Walker obtained in [2] a generalization of the Borsuk-Ulam theorem. The purpose of this note is to prove a $\mod q$ version of Walker’s theorem.

References

N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
James W. Walker, A homology version of the Borsuk-Ulam theorem, Amer. Math. Monthly 90 (1983), no. 7, 466–468. MR 711647, DOI 10.2307/2975728