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Graduate Texts in Mathematics

Introduction to Smooth Manifolds

Authors: Lee, John

  • New edition extensively revised and clarified, and topics have been substantially rearranged
  • Introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier in the text
  • Added topics include  Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures
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Hardcover $99.00
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  • ISBN 978-1-4419-9981-8
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  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
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  • ISBN 978-1-4899-9475-2
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About this Textbook

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 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 first-order 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.

About the authors

John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of four previous Springer books: the first edition (2003) of Introduction to Smooth Manifolds, the first edition (2000) and second edition (2010) of Introduction to Topological Manifolds, and Riemannian Manifolds: An Introduction to Curvature (1997).

Reviews

From the reviews of the second edition:

“It starts off with five chapters covering basics on smooth manifolds up to submersions, immersions, embeddings, and of course submanifolds. … the book under review is laden with excellent exercises that significantly further the reader’s understanding of the material, and Lee takes great pains to motivate everything well all the way through … . a fine graduate-level text for differential geometers as well as people like me, fellow travelers who always wish they knew more about such a beautiful subject.” (Michael Berg, MAA Reviews, October, 2012)


Table of contents (22 chapters)

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4419-9982-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4419-9981-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4899-9475-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Smooth Manifolds
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
218
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4419-9982-5
DOI
10.1007/978-1-4419-9982-5
Hardcover ISBN
978-1-4419-9981-8
Softcover ISBN
978-1-4899-9475-2
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XVI, 708
Topics