Chapter VIII

Integration of Exterior Forms


Orientable manifolds; Integration of forms in Euclidean space; Simplices; Chains; Boundary operator; Coboundary operator; Chain complex; Integration of forms on manifolds; Stokes' theorem; Conservation laws; Cohomology of de Rham; Cohomology groups; Homology groups; de Rham's theorem; Mayer-Vietoris sequence; Mayer-Vietoris' theorem; Harmonic forms; Theory of Hodge-de Rham; Hodge's decomposition theorem; Poincaré duality

8.1 Scope of the Chapter

In this chapter, the integral of an exterior differential form over a submanifold of a given manifold, whose dimension is equal to the degree of the exterior form, is treated as a linear operator assigning a real number to that form. As is well known, the ...

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