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Elements of Homology Theory

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The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Author(s): V. V. Prasolov
Series: Graduate Studies in Mathematics 81
Publisher: American Mathematical Society
Year: 2007

Language: English
Pages: x+418

Chapter 1. Simplicial homology
Chapter 2. Cohomology rings
Chapter 3. Applications of simplicial homology
Chapter 4. Singular homology
Chapter 5. Čech cohomology and de Rham cohomology
Chapter 6. Miscellany
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