An introduction to differential manifolds

Bibliographic Information

An introduction to differential manifolds

Jacques Lafontaine

(Grenoble sciences)

Springer, c2015

Other Title

Introduction aux variétés différentielles

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Note

"Based on translation from the French language edition: 'Introduction aux variétés différentielles' (2ème édition) by Jacques Lafontaine"--T.p. verso

"Selected by Grenoble sciences"--Cover

Includes bibliographical references and index

Description and Table of Contents

Description

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. In particular, the introduction of "abstract" notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. 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. The original French text Introduction aux varietes differentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Table of Contents

Differential Calculus.- Manifolds: The Basics.- From Local to Global.- Lie Groups.- Differential Forms.- Integration and Applications.- Cohomology and Degree Theory.- Euler-Poincare and Gauss-Bonnet.

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Details

  • NCID
    BB19421402
  • ISBN
    • 9783319207346
  • LCCN
    2015946989
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    fre
  • Place of Publication
    Cham
  • Pages/Volumes
    xix, 395 p.
  • Size
    25 cm
  • Parent Bibliography ID
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