Holomorphic Curves In Low Dimensions PDF Download
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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 | : Chris Wendl |
Publisher | : Cambridge University Press |
Total Pages | : 198 |
Release | : 2020-03-26 |
Genre | : Mathematics |
ISBN | : 1108759580 |
Download Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory Book in PDF, ePub and Kindle
Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.
Author | : Chen-Han Sung |
Publisher | : |
Total Pages | : 164 |
Release | : 1975 |
Genre | : |
ISBN | : |
Download Contributions to Holomorphic Curves in Complex Manifolds Book in PDF, ePub and Kindle
Author | : S. K. Donaldson |
Publisher | : Cambridge University Press |
Total Pages | : 277 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0521399785 |
Download Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces Book in PDF, ePub and Kindle
Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.
Author | : Chris Wendl |
Publisher | : Cambridge University Press |
Total Pages | : 197 |
Release | : 2020-03-26 |
Genre | : Mathematics |
ISBN | : 1108497403 |
Download Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory Book in PDF, ePub and Kindle
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Author | : Casim Abbas |
Publisher | : Springer |
Total Pages | : 322 |
Release | : 2019-03-29 |
Genre | : Mathematics |
ISBN | : 3030118037 |
Download Holomorphic Curves and Global Questions in Contact Geometry Book in PDF, ePub and Kindle
This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory. An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9). The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors.
Author | : Hongxi Wu |
Publisher | : Princeton University Press |
Total Pages | : 251 |
Release | : 1970-02-21 |
Genre | : Mathematics |
ISBN | : 0691080739 |
Download The Equidistribution Theory of Holomorphic Curves Book in PDF, ePub and Kindle
This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.
Author | : Olivier Collin |
Publisher | : American Mathematical Soc. |
Total Pages | : 353 |
Release | : 2020-12-14 |
Genre | : Education |
ISBN | : 147045209X |
Download Characters in Low-Dimensional Topology Book in PDF, ePub and Kindle
This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2–6, 2018, at Université du Québec à Montréal, Montréal, Québec, Canada. Boyer's contributions to research in low-dimensional geometry and topology, and to the Canadian mathematical community, were recognized during the conference. The articles cover a broad range of topics related, but not limited, to the topology and geometry of 3-manifolds, properties of their fundamental groups and associated representation varieties.
Author | : Christoph Hummel |
Publisher | : Birkhäuser |
Total Pages | : 136 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034889526 |
Download Gromov’s Compactness Theorem for Pseudo-holomorphic Curves Book in PDF, ePub and Kindle
This book presents the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities.
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.