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Differential Topology

Victor Guillemin Massachusetts Institute of Technology, Cambridge, MA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-5193-7
Product Code: CHEL/370.H
List Price: $45.00 MAA Member Price:$40.50
AMS Member Price: $40.50 Electronic ISBN: 978-1-4704-1135-0 Product Code: CHEL/370.H.E List Price:$42.00
MAA Member Price: $37.80 AMS Member Price:$33.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $67.50 MAA Member Price:$60.75
AMS Member Price: $60.75 Click above image for expanded view Differential Topology Victor Guillemin Massachusetts Institute of Technology, Cambridge, MA AMS Chelsea Publishing: An Imprint of the American Mathematical Society Available Formats:  Hardcover ISBN: 978-0-8218-5193-7 Product Code: CHEL/370.H  List Price:$45.00 MAA Member Price: $40.50 AMS Member Price:$40.50
 Electronic ISBN: 978-1-4704-1135-0 Product Code: CHEL/370.H.E
 List Price: $42.00 MAA Member Price:$37.80 AMS Member Price: $33.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$67.50 MAA Member Price: $60.75 AMS Member Price:$60.75
• Book Details

AMS Chelsea Publishing
Volume: 3701974; 222 pp
MSC: 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.

Readership

Undergraduate and graduate students interested in differential topology

• Table of Contents

• 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
• Additional Material

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Volume: 3701974; 222 pp
MSC: 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.

Readership

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
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