On the Homotopy Type of Stiefel Manifolds

  title={On the Homotopy Type of Stiefel Manifolds},
  author={Ioan Mackenzie James},
  • I. James
  • Published 1 June 1971
  • Mathematics
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. 
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