**AMS Chelsea Publishing**

Volume: 370;
1974;
222 pp;
Hardcover

MSC: Primary 53; 57; 58;

Print ISBN: 978-0-8218-5193-7

Product Code: CHEL/370.H

List Price: $42.00

Individual Member Price: $37.80

**Electronic ISBN: 978-1-4704-1135-0
Product Code: CHEL/370.H.E**

List Price: $42.00

Individual Member Price: $33.60

#### Supplemental Materials

# Differential Topology

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*Victor Guillemin; Alan Pollack*

Differential Topology provides an elementary and intuitive
introduction to the study of smooth manifolds. In the years since its
first publication, Guillemin and Pollack's book has become a standard text
on the subject. It is a jewel of mathematical exposition, judiciously
picking exactly the right mixture of detail and generality to display the
richness within.

The text is mostly self-contained, requiring only undergraduate
analysis and linear algebra. By relying on a unifying
idea—transversality—the authors are able to avoid the use
of big machinery or ad hoc techniques to establish the main
results. In this way, they present intelligent treatments of important
theorems, such as the Lefschetz fixed-point theorem, the
Poincaré–Hopf index theorem, and Stokes theorem.

The book has a wealth of exercises of various types. Some are
routine explorations of the main material. In others, the students are
guided step-by-step through proofs of fundamental results, such as the
Jordan-Brouwer separation theorem. An exercise section in Chapter 4
leads the student through a construction of de Rham cohomology and a
proof of its homotopy invariance.

The book is suitable for either an introductory graduate course or an
advanced undergraduate course.

#### Readership

Undergraduate and graduate students interested in differential topology

#### Table of Contents

# Table of Contents

## Differential Topology

- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Contents v6
- Preface to the AMS Chelsea edition ix10
- Preface xi12
- Straight forward to the student xv16
- Table of symbols xvii18
- Manifolds and smooth maps 120
- Transversality and intersection 5776
- Oriented intersection theory 94113
- Integration on manifolds 151170
- Appendix 1. Measure zero and Sard’s theorem 202221
- Appendix 2. Classification of compact one-manifolds 208227
- Bibliography 212231
- Index 217236
- Back Cover Back Cover1242