Introduction to smooth manifolds
 Author/Creator
 Lee, John M., 1950
 Language
 English.
 Edition
 2nd ed.
 Imprint
 New York ; London : Springer, 2013.
 Physical description
 xv, 708 p. : ill ; 24 cm.
 Series
 Graduate texts in mathematics ; 218.
Access
Available online

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QA613 .L44 2013

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QA613 .L44 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 675677) and indexes.
 Contents

 Preface. 1 Smooth Manifolds. 2 Smooth Maps. 3 Tangent Vectors. 4 Submersions, Immersions, and Embeddings. 5 Submanifolds. 6 Sard's Theorem. 7 Lie Groups. 8 Vector Fields. 9 Integral Curves and Flows. 10 Vector Bundles. 11 The Cotangent Bundle. 12 Tensors. 13 Riemannian Metrics. 14 Differential Forms. 15 Orientations. 16 Integration on Manifolds. 17 De Rham Cohomology. 18 The de Rham Theorem. 19 Distributions and Foliations. 20 The Exponential Map. 21 Quotient Manifolds. 22 Symplectic Manifolds. Appendix A: Review of Topology. Appendix B: Review of Linear Algebra. Appendix C: Review of Calculus. Appendix D: Review of Differential Equations. References. Notation Index. Subject Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book is an introductory graduatelevel textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of firstorder partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
(source: Nielsen Book Data)
Subjects
 Subject
 Manifolds (Mathematics)
Bibliographic information
 Publication date
 2013
 Responsibility
 John M. Lee.
 Series
 Graduate texts in mathematics ; 218
 ISBN
 9781441999818 (hbk.)
 1441999817 (hbk.)