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＜電子ブック＞
An Introduction to Manifolds / by Loring W. Tu
(Universitext. ISSN:21916675)

版	2nd ed. 2011.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2011
大きさ	XVIII, 410 p. 124 illus., 1 illus. in color : online resource
著者標目	*Tu, Loring W author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) LCSH:Global analysis (Mathematics) LCSH:Geometry, Differential FREE:Manifolds and Cell Complexes FREE:Global Analysis and Analysis on Manifolds FREE:Differential Geometry
一般注記	Preface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." HTTP:URL=https://doi.org/10.1007/978-1-4419-7400-6

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