**Graduate Studies in Mathematics**

Volume: 74;
2006;
331 pp;
Hardcover

MSC: Primary 57;

**Print ISBN: 978-0-8218-3809-9
Product Code: GSM/74**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-1153-4
Product Code: GSM/74.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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#### Supplemental Materials

# Elements of Combinatorial and Differential Topology

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*V. V. Prasolov*

Modern topology uses very diverse methods. This book is
devoted largely to methods of combinatorial topology, which reduce the study of
topological spaces to investigations of their partitions into elementary sets,
and to methods of differential topology, which deal with smooth manifolds and
smooth maps. Many topological problems can be solved by using either of these
two kinds of methods, combinatorial or differential. In such cases, both
approaches are discussed.

One of the main goals of this book is to advance as far as possible in the
study of the properties of topological spaces (especially manifolds) without
employing complicated techniques. This distinguishes it from the majority of
other books on topology.

The book contains many problems; almost all of them are supplied with hints
or complete solutions.

#### Readership

Advanced undergraduates and graduate students interested in combinatorial and differential topology.

#### Reviews & Endorsements

This book is a tour de force introduction to combinatorial and differential topology ... The author strikes a perfect balance between rigor and intuition, which allows him to delve much deeper into the chosen topics than is customary for an introductory topology course.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Elements of Combinatorial and Differential Topology

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Notation xi12 free
- Basic Definitions 114 free
- Chapter 1. Graphs 518
- Chapter 2. Topology in Euclidean Space 5568
- Chapter 3. Topological Spaces 87100
- Chapter 4. Two-Dimensional Surfaces, Coverings, Bundles, and Homotopy Groups 139152
- Chapter 5. Manifolds 181194
- Chapter 6. Fundamental Groups 257270
- Hints and Solutions 291304
- Bibliography 317330
- Index 325338
- Back Cover Back Cover1348