Stability Properties of Vector Bundles
Two vector bundles ξ and η are called s-equivalent provided ξ ⨁θ n and η ⨁θ 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 \(\tilde K\).
KeywordsVector Bundle Commutative Diagram Isomorphism Class Commutative Semigroup Homotopy Classification
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