Description: Holomorphic Curves in Low Dimensions by Chris Wendl 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 McDuffs 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 FORMAT Paperback LANGUAGE English CONDITION Brand New Back Cover 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 McDuffs 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 Author Biography Chris Wendl 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. Table of Contents 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. Review "The book is well-written, well-referenced … . Anyone interested in McDuffs characterization of rational and ruled symplectic 4-manifolds or her theorem that says uniruled => rational/ruled should find this book quite useful." (David E. Hurtubise, zbMATH 1432.57055, 2020) Review Quote "The book is well-written, well-referenced ... . Anyone interested in McDuffs characterization of rational and ruled symplectic 4-manifolds or her theorem that says uniruled => rational/ruled should find this book quite useful." (David E. Hurtubise, zbMATH 1432.57055, 2020) Feature 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 symplectic 4-manifolds Illustrates the connection between McDuffs classic results on rational/ruled surfaces and more recent developments involving symplectic fillings of contact 3-manifolds and the Weinstein conjecture Offers a concise survey of the essential analytical results in the theory of punctured holomorphic curves Details ISBN3319913697 Author Chris Wendl Publisher Springer International Publishing AG Series Lecture Notes in Mathematics Year 2018 Edition 1st ISBN-10 3319913697 ISBN-13 9783319913698 Format Paperback Imprint Springer International Publishing AG Subtitle From Symplectic Ruled Surfaces to Planar Contact Manifolds Place of Publication Cham Country of Publication Switzerland Pages 294 Publication Date 2018-06-29 DEWEY 516.36 Short Title Holomorphic Curves in Low Dimensions Language English DOI 10.1007/978-3-319-91371-1 Series Number 2216 UK Release Date 2018-06-29 Edition Description 1st ed. 2018 Audience Professional & Vocational Illustrations 31 Illustrations, color; 2 Illustrations, black and white; XIII, 294 p. 33 illus., 31 illus. in color. 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ISBN-13: 9783319913698
Book Title: Holomorphic Curves in Low Dimensions
Number of Pages: 294 Pages
Language: English
Publication Name: Holomorphic Curves in Low Dimensions: from Symplectic Ruled Surfaces to Planar Contact Manifolds
Publisher: Springer International Publishing Ag
Publication Year: 2018
Subject: Mathematics
Item Height: 235 mm
Item Weight: 4686 g
Type: Textbook
Author: Chris Wendl
Item Width: 155 mm
Format: Paperback
