A Course On Holomorphic Discs PDF Download
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Author | : Hansjörg Geiges |
Publisher | : Springer Nature |
Total Pages | : 203 |
Release | : 2023-08-07 |
Genre | : Mathematics |
ISBN | : 3031360648 |
Download A Course on Holomorphic Discs Book 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.
Author | : Saeed Zakeri |
Publisher | : Princeton University Press |
Total Pages | : 442 |
Release | : 2021-11-02 |
Genre | : Mathematics |
ISBN | : 0691207585 |
Download A Course in Complex Analysis Book 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"--
Author | : Chris Wendl |
Publisher | : Springer |
Total Pages | : 294 |
Release | : 2018-06-28 |
Genre | : Mathematics |
ISBN | : 3319913719 |
Download Holomorphic Curves in Low Dimensions Book 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
Author | : Kai Zehmisch |
Publisher | : |
Total Pages | : 276 |
Release | : 2009 |
Genre | : |
ISBN | : |
Download Singularities and Self-intersections of Holomorphic Discs Book in PDF, ePub and Kindle
Author | : Franc Forstnerič |
Publisher | : |
Total Pages | : 0 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Holomorphic Discs with Dense Images Book in PDF, ePub and Kindle
Author | : Dusa McDuff |
Publisher | : American Mathematical Soc. |
Total Pages | : 744 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0821887467 |
Download J-holomorphic Curves and Symplectic Topology Book in PDF, ePub and Kindle
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.
Author | : Franc Forstnerič |
Publisher | : |
Total Pages | : 17 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download Proper Holomorphic Discs in C2 Book in PDF, ePub and Kindle
Author | : Wilhelm Klingenberg |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
Download Holomorphic Discs in the Space of Oriented Lines Via Mean Curvature Flow and Applications Book in PDF, ePub and Kindle
Author | : Dusa McDuff |
Publisher | : American Mathematical Soc. |
Total Pages | : 220 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821803328 |
Download $J$-Holomorphic Curves and Quantum Cohomology Book in PDF, ePub and Kindle
J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.
Author | : Franc Forstnerič |
Publisher | : |
Total Pages | : 14 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download Embedding Holomorphic Discs Through Discrete Sets Book in PDF, ePub and Kindle