Whitney Sum

An operation that takes two vector bundles over a fixed space and produces a new vector bundle over the same space. If E_1 and E_2 are vector bundles over B, then the Whitney sum E_1 direct sum E_2 is the vector bundle over B such that each fiber over B is naturally the direct sum of the E_1 and E_2 fibers over B.

The Whitney sum is therefore the fiber for fiber direct sum of the two bundles E_1 and E_2. An easy formal definition of the Whitney sum is that E_1 direct sum E_2 is the pull-back bundle of the diagonal map from B to B×B, where the bundle over B×B is E_1×E_2.

See also

Bundle, Fiber, Vector Bundle

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Cite this as:

Weisstein, Eric W. "Whitney Sum." From MathWorld--A Wolfram Web Resource.

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