{"product_id":"holomorphic-curves-in-low-dimensions-from-symplectic-ruled-surfaces-to-planar-contact-manifolds-paperback","title":"Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds - Paperback","description":"\u003cp\u003eby \u003cb\u003eChris Wendl\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. \u003c\/p\u003e 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.\u003cp\u003e\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eThis book is also part of the \u003ci\u003eVirtual Series on Symplectic Geometry\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003ehttp: \/\/www.springer.com\/series\/16019\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.\u003c\/p\u003eThe 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.\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book is also part of the \u003ci\u003eVirtual Series on Symplectic Geometry\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ehttp: \/\/www.springer.com\/series\/16019\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eChris Wendl\u003c\/b\u003e is known among symplectic topologists for contributions to the study of symplectic fillability of contact manifolds, and for transversality results in the theory of pseudoholomorphic curves. He is currently Professor of Differential Geometry and Global Analysis at the Humboldt University in Berlin, and is also the author of two other forthcoming books on holomorphic curves and symplectic field theory.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 294\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.65 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e June 29, 2018\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51794697978144,"sku":"9783319913698","price":105.28,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/9e08381ac92b91215aa685af5e46baae.webp?v=1780731283","url":"https:\/\/ebocreations.com\/products\/holomorphic-curves-in-low-dimensions-from-symplectic-ruled-surfaces-to-planar-contact-manifolds-paperback","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}