In differential geometry, the tensor product of vector bundles E, F (over the same space X) is a vector bundle, denoted by E ⊗ F, whose fiber over each point x ∈ X is the tensor product of vector spaces Ex ⊗ Fx.
Thus, the set of the isomorphism classes of all line bundles on some topological space X forms an abelian group called the Picard group of X.
One can also define a symmetric power and an exterior power of a vector bundle in a similar way.
is a differential p-form with values in a vector bundle E.
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