On complex Stiefel manifolds
- 1 January 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 61 (1) , 81-103
- https://doi.org/10.1017/s0305004100038688
Abstract
We shall study the following complex Stiefel fibring:.In particular we shall study the problem: for what values of n and k does the fibring(1.1) admit a cross-section? A necessary condition for the existence of a cross-section has been found by Atiyah and Todd (8). We shall show (Theorem 1.1 below) that the condition of Atiyah and Todd is sufficient (as well as necessary) for the existence of a cross-section. The problem stated above is therefore completely solved.Keywords
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