Simplicial Homology and De Rham’s Theorem

After giving the necessary background in simplicial homology and cohomology, we will state Stokes’s theorem and show that integration of differential forms on a smooth, triangulable manifold M provides us with a homomorphism from the De Rham cohomology of M to the simplicial cohomology of M . De Rham’s theorem, which claims that this homomorphism is in fact an isomorphism, will then be stated and proved.