Introduction to Smooth Manifolds

John Lee

ISBN 10: 1489994750 / ISBN 13: 9781489994752

Editore: Springer New York, Springer US Sep 2014, 2014

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Neuware -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 fewnew 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 724 pp. Englisch.

Codice articolo 9781489994752

Dati bibliografici

• Titolo: Introduction to Smooth Manifolds
• Editore: Springer New York, Springer US Sep 2014
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 1489994750
• ISBN 13: 9781489994752
• Rilegatura: Taschenbuch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 39 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 39 millimetri di profondità
• Peso: 1077 grammi

Descrizione articolo

Riassunto

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 fewnew 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.

Informazioni sull?autore

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) ofIntroduction to Smooth Manifolds, the first edition (2000) and second edition (2010) ofIntroduction to Topological Manifolds, and Riemannian Manifolds: An Introduction to Curvature(1997).