De Rham Theorem

A theorem establishing a canonical isomorphism between the de Rham cohomology of a smooth manifold (cohomology computed from differential forms modulo exact forms) and its singular cohomology with real coefficients, thus identifying differential-form invariants with topological cohomology classes.

A theorem identifying the de Rham cohomology of a smooth manifold, defined via differential forms, with its singular (or simplicial) cohomology with real coefficients, via the integration pairing.

A fundamental result asserting an isomorphism between the cohomology of the complex of smooth differential forms on a smooth manifold (de Rham cohomology) and the singular (or sheaf) cohomology with real coefficients; the isomorphism respects algebraic structure such as cup products.