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Introduction to smooth manifolds

Author: John M Lee
Publisher: New York : Springer, ©2003.
Series: Graduate texts in mathematics, 218.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is an introductory graduate-level textbook on the theory of smooth manifolds, for 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. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lee, John M., 1950-
Introduction to smooth manifolds.
New York : Springer, ©2003
(DLC) 2002070454
(OCoLC)49681196
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John M Lee
ISBN: 9780387217529 0387217525 0387954953 9780387954950 1280189789 9781280189784 0387954481 9780387954486
OCLC Number: 666929817
Description: 1 online resource (xvii, 628 pages) : illustrations.
Contents: Preface --
Smooth Manifolds --
Smooth Maps --
Tangent Vectors --
Vector Fields --
Vector Bundles --
The Cotangent Bundle --
Submersions, Immersions, and Embeddings --
Submanifolds --
Embedding and Approximation Theorems --
Lie Group Actions --
Tensors --
Differential Forms --
Orientations --
Integration on Manifolds --
De Rham Cohomology --
The De Rham Theorem --
Integral Curves and Flows --
Lie Derivatives --
Integral Manifolds and Foliations --
Lie Groups and Their Lie Algebras --
Appendix: Review of Prerequisites --
References --
Index.
Series Title: Graduate texts in mathematics, 218.
Responsibility: John M. Lee.

Abstract:

This book is an introductory graduate-level textbook on the theory of smooth manifolds, for 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. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential geometry," in this book the author has decided to avoid use of this term because it applies more specifically to the study of smooth manifolds endowed with some extra structure, such as a Riemannian metric, a symplectic structure, a Lie group structure, or a foliation, and of the properties that are invariant under maps that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth.

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