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Complex bundles with two sections

Published online by Cambridge University Press:  24 October 2008

Elmer Rees
Elmer Rees
Affiliation:
University College of Swansea, Wales
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Extract

Atiyah(2) defined the geometrical dimension of an element to be less than k + 1 (g dim (x) ≤ k) if there is a k-dimensional bundle over X whose stable equivalence class is x. If ξ is an n-plane complex bundle over X, we say that it has r sections if there is an (n − r)-plane bundle η such that ξ is isomorphic to η ⊕ εr where εr is the trivial r-plane bundle over X. If X has dimension 2n or less, then ξ has r sections if and only if g dim (ξ − n) ≤ n − r.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 457 - 462
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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