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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

14 votes

Why differential forms are important?

From a more topological viewpoint, I think it is worth reading the famous paper of Dennis Sullivan, Infinitesimal computations in topology (Publications Mathématiques de l'IHES, 1977), in which he bui …