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" Introduction to smooth manifolds / "
John M. Lee.
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BL
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| Record Number
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627704
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dltt
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| Main Entry
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Lee, John M.,1950-
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| Title & Author
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Introduction to smooth manifolds /\ John M. Lee.
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| Publication Statement
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New York :: Springer,, c2003.
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| Series Statement
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Graduate texts in mathematics ;; 218
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| Page. NO
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xvii, 628 p. :: ill. ;; 25 cm.
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| ISBN
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0387954953 (hardcover : acid-free paper)
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: 9780387954950 (hardcover : acid-free paper)
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: 0387954481 (softcover : acid-free paper)
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: 9780387954486 (softcover : acid-free paper)
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| Bibliographies/Indexes
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Includes bibliographical references (p. [597]-599) and index.
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| Contents
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1. Smooth Manifolds -- 2. Smooth Maps -- 3. Tangent Vectors -- 4. Vector Fields -- 5. Vector Bundles -- 6. Cotangent Bundle -- 7. Submersions, Immersions, and Embeddings -- 8. Submanifolds -- 9. Lie Group Actions -- 10. Embedding and Approximation Theorems -- 11. Tensors -- 12. Differential Forms -- 13. Orientations -- 14. Integration on Manifolds -- 15. De Rham Cohomology -- 16. de Rham Theorem -- 17. Integral Curves and Flows -- 18. Lie Derivatives -- 19. Integral Manifolds and Foliations -- 20. Lie Groups and Their Lie Algebras -- App. Review of Prerequisites.
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| Abstract
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"This book is an introductory graduate-level 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 convectors, 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. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis."--BOOK JACKET.
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| Subject
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Manifolds (Mathematics)
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| LC Classification
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QA613.L44 2003
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