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On the homotopy type of Siefel manifolds


Author: I. M. James
Journal: Proc. Amer. Math. Soc. 29 (1971), 151-158
MSC: Primary 55.40; Secondary 57.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0275427-3
MathSciNet review: 0275427
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Abstract: Suppose that we have a fibre bundle where the total space has the same homotopy type as the product of the fibre and the base. When can we conclude that the bundle is trivial, in the sense of fibre bundle theory? This question arises in the classification theory of Hopf homogeneous spaces, especially in relation to Stiefel manifolds. Results are proved, using cohomology operations, which answer the question in some cases.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275427-3
Keywords: Stiefel manifold, homotopy type, cross-section, Steenrod square, secondary cohomology operation, Whitehead product, Hopf construction, Hopf homogeneous space, fibration
Article copyright: © Copyright 1971 American Mathematical Society

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