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Introduction to differential manifolds / Jacques Lafontaine.

By: Series: Grenoble sciencesPublication details: Cham : Springer, 2015.Description: xix, 395 p. ; illustrationsISBN:
  • 9783319207346
Subject(s): DDC classification:
  • 515.36 23 L166
Contents:
1. Differential Calculus -- 2. Manifolds: The Basics -- 3. From Local to Global -- 4. Lie Groups -- 5. Differential Forms -- 6. Integration and Applications -- 7. Cohomology and Degree Theory -- 8. Euler-Poincaré and Gauss-Bonnet -- Appendix -- Bibliography -- Index.
Summary: This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory.
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Includes bibliographical references and index,

1. Differential Calculus --
2. Manifolds: The Basics --
3. From Local to Global --
4. Lie Groups --
5. Differential Forms --
6. Integration and Applications --
7. Cohomology and Degree Theory --
8. Euler-Poincaré and Gauss-Bonnet --
Appendix --
Bibliography --
Index.

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory.

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