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Holomorphic Curves in Low Dimensions : From Symplectic Ruled Surfaces to Planar Contact Manifolds / by Chris Wendl
(Lecture Notes in Mathematics. ISSN:16179692 ; 2216)
版 | 1st ed. 2018. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2018 |
大きさ | XIII, 294 p. 33 illus., 31 illus. in color : online resource |
著者標目 | *Wendl, Chris author SpringerLink (Online service) |
件 名 | LCSH:Geometry, Differential LCSH:Manifolds (Mathematics) LCSH:Global analysis (Mathematics) FREE:Differential Geometry FREE:Manifolds and Cell Complexes FREE:Global Analysis and Analysis on Manifolds |
一般注記 | 1 Introduction -- 2 Background on Closed Pseudoholomorphic Curves -- 3 Blowups and Lefschetz Fibrations -- 4 Compactness -- 5 Exceptional Spheres -- 6 Rational and Ruled Surfaces -- 7 Uniruled Symplectic 4-Manifolds -- 8 Holomorphic Curves in Symplectic Cobordisms -- 9 Contact 3-Manifolds and Symplectic Fillings -- Appendix -- Bibliography -- Index This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019 HTTP:URL=https://doi.org/10.1007/978-3-319-91371-1 |
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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 | 9783319913711 |
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EB00210830 |
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