Differentiable Manifolds/De Rham cohomology

the differentiable forms of a differentiable manifold and the Cartan derivative constitute a cochain complex Let be a differentiable manifold of class . Then the diagram constitutes a chain complex of modules over , where shall denote the Cartan derivative. This follows immediately from the fact that applying the Cartan derivative twice always yields zero. de Rham cohomology Let be a differentiable manifold of class . The cohomology arising from the chain complex is called de Rham cohomology. The -th -module of this cohomology is commonly denoted .