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A Course on Holomorphic Discs

2023-08-07 Mathematics
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Release : 2023-08-07
Genre : Mathematics
Kind : eBook
Book Rating : 648/5 ( reviews)

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Book Synopsis A Course on Holomorphic Discs by : Hansjörg Geiges

Download or read book A Course on Holomorphic Discs written by Hansjörg Geiges. This book was released on 2023-08-07. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov’s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology. /divThis text can be used as the basis for a graduate course, and it is also immensely suitable for independent study. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed. This book is also part of the Virtual Series on Symplectic Geometry.

Holomorphic Curves in Low Dimensions

2018-06-28 Mathematics
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Release : 2018-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 719/5 ( reviews)

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Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl

Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl. This book was released on 2018-06-28. Available in PDF, EPUB and Kindle. Book excerpt: 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

J-holomorphic Curves and Symplectic Topology

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 467/5 ( reviews)

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Book Synopsis J-holomorphic Curves and Symplectic Topology by : Dusa McDuff

Download or read book J-holomorphic Curves and Symplectic Topology written by Dusa McDuff. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

Singularities and Self-intersections of Holomorphic Discs

2009
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Release : 2009
Genre :
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Book Synopsis Singularities and Self-intersections of Holomorphic Discs by : Kai Zehmisch

Download or read book Singularities and Self-intersections of Holomorphic Discs written by Kai Zehmisch. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

Holomorphic Discs with Dense Images

2004
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Release : 2004
Genre :
Kind : eBook
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Book Synopsis Holomorphic Discs with Dense Images by : Franc Forstnerič

Download or read book Holomorphic Discs with Dense Images written by Franc Forstnerič. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt:

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