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Graduate Texts in Mathematics Ser.: Introduction to Topological Manifolds by John M. Lee (2010, Hardcover)
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Publication Date : Dec 28 2010.
- Buy It NowIntroduction to Topological Manifolds (Graduate Texts in Mathematics, 202) by L
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-101441979395
ISBN-139781441979391
eBay Product ID (ePID)99566603
Product Key Features
Number of PagesXvii, 433 Pages
Publication NameIntroduction to Topological Manifolds
LanguageEnglish
Publication Year2010
SubjectTopology
TypeTextbook
AuthorJohn M. Lee
Subject AreaMathematics
SeriesGraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight62.8 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
ReviewsFrom 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)
Dewey Edition22
Series Volume Number202
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal514.34
Table Of ContentPreface.- 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.
SynopsisThis book is an introduction to manifolds at the beginning graduate level. 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. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. 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. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author's book Introduction to Smooth Manifolds is meant to act as a sequel to this book., 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., 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.
LC Classification NumberQA613-613.8
