

Hardcover ISBN: | 978-0-8218-5193-7 |
Product Code: | CHEL/370.H |
List Price: | $69.00 |
MAA Member Price: | $62.10 |
AMS Member Price: | $62.10 |
eBook ISBN: | 978-1-4704-1135-0 |
Product Code: | CHEL/370.H.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |
Hardcover ISBN: | 978-0-8218-5193-7 |
eBook: ISBN: | 978-1-4704-1135-0 |
Product Code: | CHEL/370.H.B |
List Price: | $134.00 $101.50 |
MAA Member Price: | $120.60 $91.35 |
AMS Member Price: | $114.10 $91.35 |


Hardcover ISBN: | 978-0-8218-5193-7 |
Product Code: | CHEL/370.H |
List Price: | $69.00 |
MAA Member Price: | $62.10 |
AMS Member Price: | $62.10 |
eBook ISBN: | 978-1-4704-1135-0 |
Product Code: | CHEL/370.H.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |
Hardcover ISBN: | 978-0-8218-5193-7 |
eBook ISBN: | 978-1-4704-1135-0 |
Product Code: | CHEL/370.H.B |
List Price: | $134.00 $101.50 |
MAA Member Price: | $120.60 $91.35 |
AMS Member Price: | $114.10 $91.35 |
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Book DetailsAMS Chelsea PublishingVolume: 370; 1974; 222 ppMSC: Primary 53; 57; 58
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.
ReadershipUndergraduate and graduate students interested in differential topology
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Table of Contents
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Chapters
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Chapter 1. Manifolds and smooth maps
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Chapter 2. Transversality and intersection
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Chapter 3. Oriented intersection theory
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Chapter 4. Integration on manifolds
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Appendix 1. Measure zero and Sard’s theorem
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Appendix 2. Classification of compact one-manifolds
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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- Additional Material
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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.
Undergraduate and graduate students interested in differential topology
-
Chapters
-
Chapter 1. Manifolds and smooth maps
-
Chapter 2. Transversality and intersection
-
Chapter 3. Oriented intersection theory
-
Chapter 4. Integration on manifolds
-
Appendix 1. Measure zero and Sard’s theorem
-
Appendix 2. Classification of compact one-manifolds