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Vector bundles that fill n-space

Published online by Cambridge University Press:  24 October 2008

S. A. Robertson  and
R. L. E. Schwarzenberger
S. A. Robertson
Affiliation:
University of Liverpool and University of Warwick
R. L. E. Schwarzenberger
Affiliation:
University of Liverpool and University of Warwick
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Extract

The idea of exact filling bundle may be described roughly as follows. Suppose that ξk is a vector bundle with fibre Rk, total space E(ξk) and base X. We say that ξk is a real k-plane bundle on X. Let in be the trivial n-plane bundle on X so that E(in) = X × Rn. A bundle monomorphism j: ξk → in defines a map : E(ξk)→Rn obtained by composition of the embedding E(ξk)→E(in) and the product projection E(in) → Rn. The map represents each fibre of ξk as a k-plane in Rn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 4 , October 1965 , pp. 869 - 875
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

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