عنوان

Introduction to smooth manifolds /

(Number (ISBN

0387954481 (softcover : acid-free paper)

(Number (ISBN

0387954953 (hardcover : acid-free paper)

(Number (ISBN

9780387954486 (softcover : acid-free paper)

(Number (ISBN

9780387954950 (hardcover : acid-free paper)

Number

dltt

Title Proper

Introduction to smooth manifolds /

General Material Designation

[Book]

First Statement of Responsibility

John M. Lee.

Place of Publication, Distribution, etc.

New York :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

c2003.

Specific Material Designation and Extent of Item

xvii, 628 p. :

Other Physical Details

ill. ;

Dimensions

25 cm.

Series Title

Graduate texts in mathematics ;

Volume Designation

218

Text of Note

Includes bibliographical references (p. [597]-599) and index.

Text of Note

1. Smooth Manifolds -- 2. Smooth Maps -- 3. Tangent Vectors -- 4. Vector Fields -- 5. Vector Bundles -- 6. Cotangent Bundle -- 7. Submersions, Immersions, and Embeddings -- 8. Submanifolds -- 9. Lie Group Actions -- 10. Embedding and Approximation Theorems -- 11. Tensors -- 12. Differential Forms -- 13. Orientations -- 14. Integration on Manifolds -- 15. De Rham Cohomology -- 16. de Rham Theorem -- 17. Integral Curves and Flows -- 18. Lie Derivatives -- 19. Integral Manifolds and Foliations -- 20. Lie Groups and Their Lie Algebras -- App. Review of Prerequisites.

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 convectors, 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. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis."--BOOK JACKET.

Manifolds (Mathematics)

QA

Class number

Book number

Lee, John M.,1950-

Date of Transaction

20140220093924.0

Electronic name

[Book]

Y