Let M be a smooth manifold. A smooth differential form of degree k is a smooth section of the k th exterior power of the cotangent bundle of M. The set of all differential k-forms on a manifold M is a vector space, often denoted Ω k (M) 19 November 2015 Updated form and guidance for use on or after 19 November 2015. 17 September 2015 Updated SET(O) guidance. 3 August 2015 Updated form published for use on or after 3 August 2015.
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