Hardcover ISBN:  9780821838129 
Product Code:  GSM/81 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $64.00 
Electronic ISBN:  9781470411589 
Product Code:  GSM/81.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $60.00 

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.

Table of Contents

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


Additional Material

Reviews

This wellwritten 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
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 Request Exam/Desk Copy
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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 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 wellwritten book is divided into six chapters and contains many problems, almost all of them being provided with hints or complete solutions.
Zentralblatt MATH