Physical description 
xvii, 628 pages : illustrations ; 25 cm. 
Series 
Graduate texts in mathematics ; 218. 

Graduate texts in mathematics ; 218.

Bibliography 
Includes bibliographical references and index. 
Contents 
1. Smooth Manifolds  2. Smooth Maps  3. Tangent Vectors  4. Vector Fields  5. Vector Bundles  6. The 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. The 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. 
Summary 
"This book is an introductory graduatelevel 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. 
Subject 
Manifolds (Mathematics)

ISBN 
0387954953 (alk. paper) 

0387954481 (paperback: alk. paper) 

0387954953 (hardcover : acidfree paper) 

0387954481 (softcover : acidfree paper) 
