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Introduction to Topological Manifolds

(Sprache: Englisch)
Autor: John M. Lee
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Extensively revised and updated, this volume provides an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas involved with further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.
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Extensively revised and updated, this volume provides an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas involved with further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.
Mehr zum Inhalt Video Autorenporträt Rezension Inhaltsverzeichnis
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Produktdetails
Produktinformationen zu „Introduction to Topological Manifolds “
Extensively revised and updated, this volume provides an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas involved with further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.
Klappentext zu „Introduction to Topological Manifolds “
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.
Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched.  The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
Inhaltsverzeichnis zu „Introduction to Topological Manifolds “
Preface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The Circle.- 9 Some Group Theory.- 10 The Seifert-Van Kampen Theorem.- 11 Covering Maps.- 12 Group Actions and Covering Maps.- 13 Homology.- Appendix A: Review of Set Theory.- Appendix B: Review of Metric Spaces.- Appendix C: Review of Group Theory.- References.- Notation Index.- Subject Index.
Autoren-Porträt von John M. Lee
John M. Lee is a professor of mathematics and the University of Washington. His previous Springer textbooks in the Graduate Texts in Mathematics include the first edition of Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Riemannian Manifolds: An Introduction.
Bibliographische Angaben

  • Autor: John M. Lee
  • 2011, 2nd Edition., XVIII, 434 Seiten, Maße: 16,4 x 24,4 cm, Gebunden, Englisch
  • Verlag: Springer US
  • ISBN-10: 1441979395
  • ISBN-13: 9781441979391

Sprache:
Englisch
Rezension zu „Introduction to Topological Manifolds “
From the reviews of the second edition:"An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. ... The author has ... fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. ... Any student who has gone through this book should be well-prepared to pursue the study of differential geometry ... ." (Mark Hunacek, The Mathematical Association of America, March, 2011)"This book is designed for first year graduate students as an introduction to the topology of manifolds. ... The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work." (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011)
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