Exterior-derivative nilpotency d circ d = 0; de Rham complex; cohomology

Exterior-derivative framework (Cartan 1899 Comptes Rendus 129, 522; de Rham 1931 Sur l'analysis situs des varietes a n dimensions; 1950 Varietes differentiables). Setup: on a smooth manifold M, the exterior derivative d: Omega^k(M) ->…