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Introduction to Topological Manifolds / by John Lee
(Graduate Texts in Mathematics. ISSN:21975612 ; 202)
版 | 2nd ed. 2011. |
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出版者 | New York, NY : Springer New York : Imprint: Springer |
出版年 | 2011 |
大きさ | XVII, 433 p : online resource |
著者標目 | *Lee, John author SpringerLink (Online service) |
件 名 | LCSH:Manifolds (Mathematics) LCSH:Algebraic topology FREE:Manifolds and Cell Complexes FREE:Algebraic Topology |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-7940-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781441979407 |
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EB00197521 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA613-613.8 DC23:514.34 |
書誌ID | 4000116859 |
ISBN | 9781441979407 |
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※2017年9月4日以降