Differentiable Manifolds
Seiten
2008
|
Reprint of the 2001 2nd ed.
Birkhauser Boston Inc (Verlag)
978-0-8176-4766-7 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-4766-7 (ISBN)
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. New to the second edition is a detailed treatment of covering spaces and the fundamental group.
Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.
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. New to the second edition is a detailed treatment of covering spaces and the fundamental group.
Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.
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*.
| Erscheint lt. Verlag | 11.1.2008 |
|---|---|
| Reihe/Serie | Modern Birkhäuser Classics |
| Zusatzinfo | XIV, 418 p. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8176-4766-X / 081764766X |
| ISBN-13 | 978-0-8176-4766-7 / 9780817647667 |
| Zustand | Neuware |
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