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The k-th exterior power of the cotangent bundle
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Every differential k-form is a global section of the k-th exterior power of the cotangent bundle. The fiber over p of this bundle is the space of alternating k-ten sors on TpM. For each coordinate chart U, phi we identify the set of all fibers over U with phi(U)x R^(n choose k). Via this we define open subsets of this set- and these open subsets give a basis for the topology on the K-th exterior power of the cotangent bundle
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