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Introduction to Topological Manifolds / by John M. Lee

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Graduate Texts in Mathematics ; 202 | SpringerLink BücherPublisher: New York, NY : Springer New York, 2011Description: Online-Ressource (XVII, 433p. 131 illus, digital)ISBN:
  • 9781441979407
Subject(s): Genre/Form: Additional physical formats: 9781441979391 | Buchausg. u.d.T.: Introduction to topological manifolds. Second edition. New York : Springer, 2011. xvii, 433 SeitenMSC: MSC: *57-01 | 55N10 | 57N65 | 57M05 | 57M10 | 57N05 | 57Q05 | 55-01 | 55Q05RVK: RVK: SI 990 | SK 350LOC classification:
  • QA613-613.8 QA613.6-613.66
DOI: DOI: 10.1007/978-1-4419-7940-7Online resources: Summary: 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.Summary: This 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.PPN: PPN: 1650743963Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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