Chapter 8

de Rham Cohomology

Abstract

We begin this chapter with some algebraic constructions that we will need later: (co) chain complexes and related matters. Then we introduce the de Rham cohomology of a smooth manifold with boundary image, which measures in a precise way the difference between closed and exact differential forms on image. Actually, we introduce the notion of a smooth pair image and consider the de Rham cohomology of a smooth pair. We develop ...

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