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Holomorphic Curves in Low Dimensions
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 t...
Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
J-holomorphic Curves and Symplectic Topology
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.
Broadcast Announcing Worktext
Broadcast Announcing Worktext provides you with the skills, techniques, and procedures necessary to enter this highly competitive field of broadcast performance. In addition to the principles of good performance, this book addresses the importance of audience and how messages change to communicate effectively to various groups. Television and radio studio environments, announcer specializations and responsibilities, and developing a broadcast delivery style are just a few of the many topics covered. Factual information is presented in brief, easy-to-digest modules and is enhanced with self-study questions and projects. The self-study provides an immediate check on the comprehension of what y...
Contact and Symplectic Topology
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
New Perspectives and Challenges in Symplectic Field Theory
This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.
Broadcast Announcing Worktext
The Broadcast Announcing Worktext provides you with the skills, techniques, and procedures necessary to enter this highly competitive field of broadcast performance. Factual information is presented in easy-to-digest modules and projects that encourage active participation. Each chapter concludes with a self-study section students can use to test themselves. The companion website illustrates techniques and concepts with audio and visual examples that help students to learn better broadcast performace techniques. New to this edition are brand new audio clips and videos, interviews with industry professionals, and updated content throughout, including a new section on social media in the news.
Lectures on Lagrangian Torus Fibrations
Comprehensive and visual introduction to the geometry of 4-dimensional symplectic manifolds via 2-dimensional almost-toric diagrams.
An Introduction to Contact Topology
This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
Research Directions in Symplectic and Contact Geometry and Topology
This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field. The volume contains both original results and survey articles, presenting ...
