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Differentiable manifolds
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Differentiable manifolds

Differentiable manifolds

Lawrence Colon

418 pages, parution le 04/12/2001 (2eme édition)

Résumé

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. {Differentiable Manifolds} is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field. The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further (optional) development of Lie theory than is customary in textbooks at this level.

Table of Contents

  • Preface to the Second Edition
  • Topological Manifolds
  • The Local Theory of Smooth Functions
  • The Global Theory of Smooth Functions
  • Flows and Foliations
  • Lie Groups and Lie Algebras
  • Covectors and 1--Forms
  • Multilinear Algebra and Tensors
  • Integration of Forms and de Rham Cohomology
  • Forms and Foliations
  • Riemannian Geometry
  • Principal Bundles
  • Appendix A. Construction of the Universal Covering
  • Appendix B. Inverse Function Theorem
  • Appendix C. Ordinary Differential Equations
  • Appendix D. The de Rham Cohomology Theorem
  • Bibliography
  • Index

Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Lawrence Colon
Parution 04/12/2001
Édition  2eme édition
Nb. de pages 418
Format 16 x 24
Couverture Relié
Poids 765g
Intérieur Noir et Blanc
EAN13 9780817641344

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