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Fibre Bundles over Spheres

Published online by Cambridge University Press:  22 January 2016

Ryoji Shizuma
Ryoji Shizuma*
Affiliation:
Nagoya University
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This note is concerned with homotopy relations in fibre bundles over spheres, in connection with my previous note.

Let R be a fibre boundle, with the n-dimensional sphere Sn as the base space and with fibres which are connected and simple in n − 1 dimension. Let further π denote the projection of R onto Sn. We take a simplicial decomposition K of Sn which is so fine that the star of each simplex lies in a coordinate neighborhood of Sn.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 1 , June 1950 , pp. 59 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1950

References

[1] Eilenberg, S., On the relation between the fundamental group of a space and the higher homotopy groups, Fund. Math., 32 (1939), 167–175.Google Scholar
[2] Hurewicz, W. Beiträge zur Topologie der Deformationen II, Proc. Akad. Amsterdam, 38(1935), 521–528.Google Scholar
[3] Hurewicz, W. and Steenrod, N., Homotopy relations in fibre spaces, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 60–64.CrossRefGoogle ScholarPubMed
[4] Shizuma, R., Homotopy properties of fibre bundles, forthcoming J. of Math, of Japan.Google Scholar
[5] Steenrod, N., The classification of sphere bunbles, Ann, of Math., 45 (1944), 294–311.Google Scholar
[6] Stiefel, E., Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigialtigkeiten, Comment. Math. Helv., 8 (1936), 3–51.Google Scholar