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Geometry of Differential Forms
 
Shigeyuki Morita University of Tokyo, Tokyo, Japan
Softcover ISBN:  978-0-8218-1045-3
Product Code:  MMONO/201
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4626-0
Product Code:  MMONO/201.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-1045-3
eBook: ISBN:  978-1-4704-4626-0
Product Code:  MMONO/201.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
Click above image for expanded view
Geometry of Differential Forms
Shigeyuki Morita University of Tokyo, Tokyo, Japan
Softcover ISBN:  978-0-8218-1045-3
Product Code:  MMONO/201
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4626-0
Product Code:  MMONO/201.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-1045-3
eBook ISBN:  978-1-4704-4626-0
Product Code:  MMONO/201.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
  • Book Details
     
     
    Translations of Mathematical Monographs
    Iwanami Series in Modern Mathematics
    Volume: 2012001; 321 pp
    MSC: Primary 57; 58;

    Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms.

    This book is a comprehensive introduction to differential forms. It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory.

    With minimal prerequisites, the book can serve as a textbook for an advanced undergraduate or a graduate course in differential geometry.

    Readership

    Advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and differential topology.

  • Table of Contents
     
     
    • Chapters
    • Manifolds
    • Differential forms
    • The de Rham theorem
    • Laplacian and harmonic forms
    • Vector bundles and characteristic classes
    • Fiber bundles and characteristic classes
    • Perspectives
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2012001; 321 pp
MSC: Primary 57; 58;

Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms.

This book is a comprehensive introduction to differential forms. It begins with a quick presentation of the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results about them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated in the book is a detailed description of the Chern-Weil theory.

With minimal prerequisites, the book can serve as a textbook for an advanced undergraduate or a graduate course in differential geometry.

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and differential topology.

  • Chapters
  • Manifolds
  • Differential forms
  • The de Rham theorem
  • Laplacian and harmonic forms
  • Vector bundles and characteristic classes
  • Fiber bundles and characteristic classes
  • Perspectives
Review Copy – for publishers of book reviews
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.