Differentiable manifolds
著者
書誌事項
Differentiable manifolds
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser, c2001
2nd ed
- [: us]
- [: gw]
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注記
First ed. published, c1993, under title of Differentiable manifolds : a first course
Includes bibliography (p. [403]-404) and index
内容説明・目次
- 巻冊次
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[: us] ISBN 9780817641344
内容説明
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.
目次
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.
- 巻冊次
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[: gw] ISBN 9783764341343
内容説明
This text is based on the full-year PhD qualifying course on differentiable manifolds, global calculus, differential geometry and related topics, given by the author at Washington University. It presupposes a good grounding in general topology and modern algebra, especially linear algebra and analogous theory of modules over a commutative, unitary ring.
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