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Differential Topology
 
Victor Guillemin Massachusetts Institute of Technology, Cambridge, MA
Differential Topology
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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
Differential Topology
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Differential Topology
Victor Guillemin Massachusetts Institute of Technology, Cambridge, MA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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
  • 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.