Simplicial Homology and De Rham's Theorem

Abstract

After giving the necessary background in simplicial homology and cohomology, we will state Stokes's theorem and show that integration of di erential 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.