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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On quaternionic James numbers and almost-quaternion substructures on the sphere


Author: Turgut Önder
Journal: Proc. Amer. Math. Soc. 86 (1982), 535-540
MSC: Primary 55S40; Secondary 53C15
MathSciNet review: 671231
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Abstract: In this paper a theorem about the relation between the divisibility of orders of obstructions to cross sectioning symplectic Stiefel manifolds and quaternionic James numbers is proved. As an application of this, the existence problem of almost-quaternion $ k$-substructures on the sphere $ {S^n}$ is solved for all $ n$ and $ k$ except for the case $ n = 4m - 3$, $ k = m - 1$ for some $ m \geqslant 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0671231-X
PII: S 0002-9939(1982)0671231-X
Keywords: Sectioning fiber spaces and bundles, almost-complex, contact, symplectic, almost product structures
Article copyright: © Copyright 1982 American Mathematical Society