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Introduction to Smooth Manifolds

BuchGebunden
708 Seiten
Englisch
Springererschienen am26.08.20122. Aufl.
Familiarizes students with the tools they need 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.mehr
Verfügbare Formate
BuchGebunden
EUR42,79
BuchKartoniert, Paperback
EUR42,79
E-BookPDF1 - PDF WatermarkE-Book
EUR53,49

Produkt

KlappentextFamiliarizes students with the tools they need 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.
Details
ISBN/GTIN978-1-4419-9981-8
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2012
Erscheinungsdatum26.08.2012
Auflage2. Aufl.
ReiheGraduate Texts in Mathematics
Seiten708 Seiten
SpracheEnglisch
Gewicht1202 g
IllustrationenXVI, 708 p.
Artikel-Nr.11739947

Inhalt/Kritik

Inhaltsverzeichnis
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.-  22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index.mehr
Kritik
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)mehr

Schlagworte

Autor

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).