Stability Properties of Vector Bundles

Abstract

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 \(\tilde K\).