Series: Translations of Mathematical Monographs. xxiv 321p paperback, burgundy and navy binding, minor wear to covers, a fresh and clean copy, no names or stamps, no traces of use, excellent condition, like new, previous owner's ephemera inserted Language: English.

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Bibliographic Details

Title

Geometry of Differential Forms.

Publisher

Providence: American Mathematical Society

Publication Date

2001

Language

English

ISBN 10

0821810456

ISBN 13

9780821810453

Binding

Paperback

Edition

1st Edition

Condition

As New

Seller catalogs

Mathematics

About this title

Synopsis

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. 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.

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