Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55.40, 57.00

Retrieve articles in all journals with MSC: 55.40, 57.00


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