Introduction to Smooth Manifolds

Graduate Texts in Mathematics

John M. Lee

628 pages, parution le 07/11/2002

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Résumé

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. 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.

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	07/11/2002
Nb. de pages	628
Format	15,5 x 23,5
Couverture	Broché
Poids	920g
Intérieur	Noir et Blanc
EAN13	9780387954486
ISBN13	978-0-387-95448-6