Warenkorb
 

Introduction to Smooth Manifolds

Graduate Texts in Mathematics 218

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 few new 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.
Rezension
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)
Portrait

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).

… weiterlesen
In den Warenkorb

Beschreibung

Produktdetails


Einband gebundene Ausgabe
Seitenzahl 708
Erscheinungsdatum 26.08.2012
Sprache Englisch
ISBN 978-1-4419-9981-8
Verlag Springer
Maße (L/B/H) 24,1/15,9/4,5 cm
Gewicht 1190 g
Abbildungen 176 schwarz-weiße Abbildungen
Auflage 2nd edition
Buch (gebundene Ausgabe, Englisch)
79,99
inkl. gesetzl. MwSt.
Sofort lieferbar
Versandkostenfrei
In den Warenkorb
PAYBACK Punkte
Ihr Feedback zur Seite
Haben Sie alle relevanten Informationen erhalten?
Vielen Dank für Ihr Feedback!
Entschuldigung, beim Absenden Ihres Feedbacks ist ein Fehler passiert. Bitte versuchen Sie es erneut.

Weitere Bände von Graduate Texts in Mathematics mehr

  • Band 212

    3125735
    Lectures on Discrete Geometry
    von J. Matousek
    Buch
    84,99
  • Band 214

    32355251
    Partial Differential Equations
    von Jürgen Jost
    Buch
    59,99
  • Band 216

    23482605
    Matrices
    von Denis Serre
    Buch
    82,99
  • Band 218

    28447439
    Introduction to Smooth Manifolds
    von John M. Lee
    Buch
    79,99
    Sie befinden sich hier
  • Band 219

    3793960
    The Arithmetic of Hyperbolic 3-Manifolds
    von Colin Maclachlan
    Buch
    88,99
  • Band 222

    40399684
    Lie Groups, Lie Algebras, and Representations
    von Brian Hall
    Buch
    59,99
  • Band 223

    4480933
    Fourier Analysis and Its Applications
    von Anders Vretblad
    Buch
    51,99

Kundenbewertungen

Es wurden noch keine Bewertungen geschrieben.