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On complex Stiefel manifolds

Published online by Cambridge University Press:  24 October 2008

J. F. Adams  and
G. Walker
J. F. Adams
Affiliation:
University of Manchester
G. Walker
Affiliation:
University of Manchester
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 81 - 103
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

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