De Rham cohomology
In differential geometry, differential forms on a smooth manifold which are exterior derivatives are called exact; and forms whose exterior derivatives are 0 are called closed.Exact forms are closed, so the vector spaces of k-forms along with the exterior derivative are a cochain complex. The vector spaces of closed forms modulo exact forms are called the de Rham cohomology groups. The wedge product endows the direct sum of these groups with a ring structure.
The general Stokes' theorem is an expression of duality between de Rham cohomology and the homology of chains.
