Whitney sum

Summary

The Whitney sum $E \oplus E'$ of two vector bundles over the same base has as fiber over each point the direct sum of the two fibers. It is the basic operation on vector bundles, and with it the isomorphism classes of vector bundles over a space form a commutative monoid. Characteristic classes behave multiplicatively under Whitney sum, which is the content of the Whitney product formula. Over a compact Hausdorff space, topological K-theory is the group completion of this monoid.