## 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 .