Whitney Sum

An operation that takes two vector bundles over a fixed space and produces a new vector bundle over the same space. If  and  are vector bundles over , then the Whitney sum  is the vector bundle over  such that each fiber over  is naturally the direct sum of the  and  fibers over .

The Whitney sum is therefore the fiber for fiber direct sum of the two bundles  and . An easy formal definition of the Whitney sum is that  is the pull-back bundle of the diagonal map from  to , where the bundle over  is .