Abstract:In Chapter 8, we show that de Rham cohomology is isomorphic to singular cohomology, PL cohomology, and sheaf cohomology. We begin in Section 8.1 by presenting some standard results in homological alge...In Chapter 8, we show that de Rham cohomology is isomorphic to singular cohomology, PL cohomology, and sheaf cohomology. We begin in Section 8.1 by presenting some standard results in homological algebra that we used to complete the proof of Theorem 5.2 by establishing the Mayer-Vietoris sequence in de Rham cohomology and by showing that de Rham cohomology is a homotopy functor. In Section 8.2, we discuss simplicial theory. In Section 8.3, we discuss singular (i.e., topological or simply TP) cohomology $$H_ * ^{{\rm{TP}}}\left( \cdot \right)$$ and $$H_{{\rm{TP}}}^ * \left( \cdot \right)$$ . In Section 8.4, we treat sheaf cohomology.Read More
Publication Year: 2015
Publication Date: 2015-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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