عنوان

Introduction to smooth manifolds /

(Number (ISBN

1441999817

(Number (ISBN

1441999825

(Number (ISBN

1489994750

(Number (ISBN

9781441999818

(Number (ISBN

9781441999825

(Number (ISBN

9781489994752

Country Code

bnb

Number

b623607

Title Proper

Introduction to smooth manifolds /

General Material Designation

[Book]

First Statement of Responsibility

John M. Lee.

Edition Statement

2nd ed.

Place of Publication, Distribution, etc.

London :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2013.

Specific Material Designation and Extent of Item

xv, 708 pages :

Other Physical Details

illustrations ;

Dimensions

24 cm

Series Title

Graduate texts in mathematics ;

Volume Designation

218

Text of Note

Includes bibliographical references (pages 675-677) and indexes.

Text of Note

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 contangent 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 -- Appendices.

0

Text of Note

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.

Title

Introduction to smooth manifolds.

International Standard Book Number

9781441999818

Manifolds (Mathematics)

Mathematics.

Manifolds (Mathematics)

QA

Number

Edition

Class number

Book number

Class number

Lee, John M.,1950-

Date of Transaction

20200617082716.0

Electronic name

[Book]

Y