Overview
- Entry point to Symplectic Field Theory (SFT)
- Entry point for the study of finite energy foliations
- Proves deep results in pseudoholomorphic curve theory
- Written by leading researchers in this area
- A must to have to graduate students entering this field of mathematical research
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“The book under review is the entry point for studying low-dimensional foliations and the symplectic field theory. … It can be seen as a perfect tool for graduate students and researchers who would like to learn about pseudoholomorphic curves in contact geometry.” (Roman Golovko, zbMATH 1431.53001, 2020)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Holomorphic Curves and Global Questions in Contact Geometry
Authors: Casim Abbas, Helmut Hofer
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-030-11803-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-11802-0Published: 15 April 2019
eBook ISBN: 978-3-030-11803-7Published: 29 March 2019
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: XII, 322
Number of Illustrations: 31 b/w illustrations, 2 illustrations in colour
Topics: Differential Geometry, Global Analysis and Analysis on Manifolds, Dynamical Systems and Ergodic Theory, Several Complex Variables and Analytic Spaces