**Graduate Studies in Mathematics**

Volume: 81;
2007;
418 pp;
Hardcover

MSC: Primary 55;

**Print ISBN: 978-0-8218-3812-9
Product Code: GSM/81**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-1-4704-1158-9
Product Code: GSM/81.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

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#### Supplemental Materials

# Elements of Homology Theory

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*V. V. Prasolov*

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.

#### Readership

Graduate students interested in algebraic topology.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Elements of Homology Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Notation ix10 free
- Chapter 1. Simplicial Homology 112 free
- Chapter 2. Cohomology Rings 5970
- Chapter 3. Applications of Simplicial Homology 111122
- Chapter 4. Singular Homology 195206
- Chapter 5. Čech Cohomology and de Rham Cohomology 263274
- Chapter 6. Miscellany 301312
- Hints and Solutions 365376
- Bibliography 403414
- Index 411422
- Back Cover Back Cover1432