A Course on Holomorphic Discs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course on Holomorphic Discs write by Hansjörg Geiges. This book was released on 2023-08-07. A Course on Holomorphic Discs available in PDF, EPUB and Kindle. 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.
A Course in Complex Analysis
A Course in Complex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Complex Analysis write by Saeed Zakeri. This book was released on 2021-11-02. A Course in Complex Analysis available in PDF, EPUB and Kindle. "This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--
Holomorphic Curves in Low Dimensions
Holomorphic Curves in Low Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Curves in Low Dimensions write by Chris Wendl. This book was released on 2018-06-28. Holomorphic Curves in Low Dimensions available in PDF, EPUB and Kindle. 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
Singularities and Self-intersections of Holomorphic Discs
Singularities and Self-intersections of Holomorphic Discs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Singularities and Self-intersections of Holomorphic Discs write by Kai Zehmisch. This book was released on 2009. Singularities and Self-intersections of Holomorphic Discs available in PDF, EPUB and Kindle.
Holomorphic Discs with Dense Images
Holomorphic Discs with Dense Images - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Discs with Dense Images write by Franc Forstnerič. This book was released on 2004. Holomorphic Discs with Dense Images available in PDF, EPUB and Kindle.
