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Elements of Homology Theory

V. V. Prasolov Independent University of Moscow, Moscow, Russia
Available Formats:
Hardcover ISBN: 978-0-8218-3812-9
Product Code: GSM/81
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $64.00 Electronic ISBN: 978-1-4704-1158-9 Product Code: GSM/81.E List Price:$75.00
MAA Member Price: $67.50 AMS Member Price:$60.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Click above image for expanded view Elements of Homology Theory V. V. Prasolov Independent University of Moscow, Moscow, Russia Available Formats:  Hardcover ISBN: 978-0-8218-3812-9 Product Code: GSM/81  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$64.00
 Electronic ISBN: 978-1-4704-1158-9 Product Code: GSM/81.E
 List Price: $75.00 MAA Member Price:$67.50 AMS Member Price: $60.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
• Book Details

Volume: 812007; 418 pp
MSC: Primary 55;

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 Čech 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.

Graduate students interested in algebraic topology.

• Chapters
• 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
• Hints and solutions

• Reviews

• This well-written book is divided into six chapters and contains many problems, almost all of them being provided with hints or complete solutions.

Zentralblatt MATH
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Volume: 812007; 418 pp
MSC: Primary 55;

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 Čech 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.

Graduate students interested in algebraic topology.

• Chapters
• 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
• Hints and solutions
• This well-written book is divided into six chapters and contains many problems, almost all of them being provided with hints or complete solutions.

Zentralblatt MATH
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