Edition 
Second edition. 
Physical description 
1 online resource (xiii, 418 pages) : illustrations. 
Series 
Modern Birkh衵ser classics 

Modern Birkh衵ser classics.

Contents 
Preface to the second edition  Acknowledgments  Chapter 1. Topological manifolds  Chapter 2. The local theory of smooth functions  Chapter 3. The global theory of smooth functions  Chapter 4. Flows and foliations  Chapter 5. Lie groups and lie algebras  Chapter 6. Covectors and 1forms  Chapter 7. Multilinear algebra and tensors  Chapter 8. Integration of forms and de Rham cohomology  Chapter 9. Forms and foliations  Chapter 10. Riemannian geometry  Chapter 11. Principal bundles  Appendix A. Construction of the universal covering  Appendix B. The inverse function theorem  Appendix C. Ordinary differential equations  Appendix D. The de Rham cohomology theorem  Bibliography  Index. 
Notes 
"Reprint of the 2001 second edition." 
Bibliography 
Includes bibliographical references and index. 
Summary 
The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by nonspecialists wishing to survey the field. The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further (optional) development of Lie theory than is customary in textbooks at this level. New to the second edition is a detailed treatment of covering spaces and the fundamental group. Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text. 
Notes 
Description based on print version record. 
Subject 
Differentiable manifolds.


Differentiable manifolds  Textbooks.


Electronic books. 
ISBN 
9780817647674 (electronic bk.) 

0817647678 (electronic bk.) 

9780817647667 
