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Author Conlon, Lawrence, 1933- author.

Title Differentiable manifolds / Lawrence Conlon.

Published Boston : Birkh衵ser, [2008]


Location Call No. Status
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 1-forms -- 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 non-specialists 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.)