Geometry to Differential Forms

ISBN-10: 0821810456

ISBN-13: 9780821810453

Edition: 2001

Authors: Shigeyuki Morita

List price: $66.00
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Description:

Since the times of Gauss, Riemann, and Poincare, 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. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning 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 is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
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Book details

List price: $66.00
Copyright year: 2001
Publisher: American Mathematical Society
Publication date: 8/28/2001
Binding: Paperback
Pages: 321
Size: 5.50" wide x 8.50" long x 1.00" tall
Weight: 0.880

Answers to exercises
Index
Manifolds Differential forms de Rham theorem
Laplacian and harmonic forms
Vector bundles and characteristic classes
Fiber bundles and characteristic classes
Perspectives Solutions
References
Index
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