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Fibre Bundles pp 111-121 | Cite as

Stability Properties of Vector Bundles

  • Dale Husemoller
Part of the Graduate Texts in Mathematics book series (GTM, volume 20)

Abstract

Two vector bundles ξ and η are called s-equivalent provided ξ ⨁θ n and ηθ m are isomorphic for some n and m where θ m denotes the m dimensional trivial vector bundle. Stable equivalence, or s-equivalence, is an equivalence relation, and the stable classes form a ring (over finite-dimensional spaces), with ⨁ inducing the addition operation and ⨂ the multiplication operation. These are the \(\tilde K\)-rings of the space. We study the relation between isomorphism and stable equivalence. Also we consider elementary properties of the cofunctor \(\tilde K\).

Keywords

Vector Bundle Commutative Diagram Isomorphism Class Commutative Semigroup Homotopy Classification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Dale Husemoller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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