Hardcover ISBN:  9780821851937 
Product Code:  CHEL/370.H 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $40.50 
Electronic ISBN:  9781470411350 
Product Code:  CHEL/370.H.E 
List Price:  $42.00 
MAA Member Price:  $37.80 
AMS Member Price:  $33.60 

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 selfcontained, 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 fixedpoint 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 stepbystep through proofs of fundamental results, such as the JordanBrouwer 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

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 onemanifolds


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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 selfcontained, 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 fixedpoint 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 stepbystep through proofs of fundamental results, such as the JordanBrouwer 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 onemanifolds