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Introducing k-form (part 1)
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We will define differential k-form as a map that sends every p to a k-covector at p. We give local expression for k-form. By viewing k-form as sections of the k-th exterior power of the cotangent bundle, we can define smooth k-forms, which can be characterized in terms of local coefficients. K-forms are multilinear over functions Pullback of k-forms commute with addition, multiplication and wedge product as well as exterior derivative
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