Introduction to Smooth Manifolds PDF ePub eBook

Books Info:

Introduction to Smooth Manifolds free pdf 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.

About 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 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).

Details Book

Author : John M. Lee
Publisher : Springer-Verlag New York Inc.
Data Published : 24 August 2012
ISBN : 1441999817
EAN : 9781441999818
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 708 pages
Age + : 15 years
Language : English
Rating :

Reviews Introduction to Smooth Manifolds



17 Comments Add a comment




Related eBooks Download


  • Differential Analysis on Complex Manifolds free pdfDifferential Analysis on Complex Manifolds

    A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds. this comprehensive. well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles)..


  • Analysis and Algebra on Differentiable Manifolds free pdfAnalysis and Algebra on Differentiable Manifolds

    This is the second edition of this best selling problem book for students. now containing over 400 completely solved exercises on differentiable manifolds. Lie theory. fibre bundles and Riemannian manifolds..


  • Differential Geometry of Manifolds free pdfDifferential Geometry of Manifolds

    From the coauthor of Differential Geometry of Curves and Surfaces. this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds..


  • Analysis on Manifolds free pdfAnalysis on Manifolds

    A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts..


  • Differential Geometry, Functional Analysis and Applications free pdfDifferential Geometry, Functional Analysis and Applications

    DIFFERENTIAL GEOMETRY. FUNCTIONAL ANALYSIS AND APPLICATIONS discusses Submanifolds theory. Fibre bundle. Harmonic morphisms. Homogeneous and symmetric spaces. Structures on manifolds..


  • Introduction to Smooth Manifolds free pdfIntroduction to Smooth Manifolds

    Audio Book Downloads. 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 manifold