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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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Why are differential forms called closed and exact?

Well, the notion of exactness lies in an algebraic background. Given a sequence of groups or R-Modules and morphisms given by arrows in the following way: ... -> A_n --f_n--> A_n+1 --f_n+1--> A_n+2 - …
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