Elements of Homology Theory

V. V. Prasolov (Autor)

Buch | Softcover

418 Seiten

2007
American Mathematical Society (Verlag)
978-1-4704-7976-3 (ISBN)

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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.

V. V. Prasolov, Independent University of Moscow, Russia

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

Erscheinungsdatum	12.06.2025
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-7976-1 / 1470479761
ISBN-13	978-1-4704-7976-3 / 9781470479763
Zustand	Neuware