Introduction to Smooth Manifolds

John M. Lee

628 pages, parution le 31/10/2002

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Résumé

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.

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

L'auteur - John M. Lee

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 Societys Centennial Research Fellowship and he is the author of two previous Springer books, Introduction to Topological Manifolds (2000) and Riemannian Manifolds: An Introduction to Curvature (1997).

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	John M. Lee
Parution	31/10/2002
Nb. de pages	628
Format	16 x 24
Couverture	Relié
Poids	1035g
Intérieur	Noir et Blanc
EAN13	9780387954950
ISBN13	978-0-387-95495-0