An Introduction to Manifolds: Second Edition (Universitext) - Softcover

Buch 73 von 261: Universitext

Tu, Loring W. W.

 
9781441973993: An Introduction to Manifolds: Second Edition (Universitext)
Softcover
ISBN 10: 1441973990 ISBN 13: 9781441973993
Verlag: Springer, 2010

Inhaltsangabe

An Introduction to Manifolds presents the theory of manifolds with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book, the reader will have the ability to compute one of the most basic topological invariants of a manifold, its de Rham cohomology.

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Über die Autorin bzw. den Autor

Loring W. Tu was born in Taipei, Taiwan, and grew up in Taiwan,Canada, and the United States. He attended McGill University and Princeton University as an undergraduate, and obtained his Ph.D. from Harvard University under the supervision of Phillip A. Griffiths. He has taught at the University of Michigan, Ann Arbor, and at Johns Hopkins University, and is currently Professor of Mathematics at Tufts University in Massachusetts. An algebraic geometer by training, he has done research at the interface of algebraic geometry,topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology. He is the coauthor with Raoul Bott of "Differential Forms in Algebraic Topology."

Von der hinteren Coverseite

Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology."

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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
1441973990
ISBN 13 
9781441973993
Einband
Taschenbuch
Auflage
2
Anzahl der Seiten
432
Kontakt zum Hersteller
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Poststr. 9
Darmstadt
64293
Deutschland

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