| 书目名称 | Holomorphic Curves in Low Dimensions | | 副标题 | From Symplectic Rule | | 编辑 | Chris Wendl | | 视频video | | | 概述 | Provides an up-to-date perspective on certain foundational results in 4-dimensional symplectic topology.Includes the first exposition aimed at graduate students on the classification of uniruled sympl | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | .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 fil | | 出版日期 | Book 2018 | | 关键词 | MSC (2010): 57R17, 32Q65; symplectic ruled surfaces; rational and ruled symplectic 4-manifolds; planar | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-91371-1 | | isbn_softcover | 978-3-319-91369-8 | | isbn_ebook | 978-3-319-91371-1Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer Nature Switzerland AG 2018 |
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发表于 2025-3-21 20:04:29
