| 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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Book DetailsGraduate Studies in MathematicsVolume: 81; 2007; 418 ppMSC: 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.ReadershipGraduate students interested in algebraic topology.
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Table of Contents
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Chapters
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Chapter 1. Simplicial homology
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Chapter 2. Cohomology rings
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Chapter 3. Applications of simplicial homology
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Chapter 4. Singular homology
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Chapter 5. Čech cohomology and de Rham cohomology
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Chapter 6. Miscellany
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Hints and solutions
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Additional Material
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Reviews
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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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- Book Details
- Table of Contents
- Additional Material
- Reviews
-
- Request Review Copy
- Request Exam/Desk Copy
- Get Permissions
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
