Lectures on Symplectic Field Theory

TL;DR

This book provides an introduction to symplectic field theory, focusing on punctured pseudoholomorphic curves, with applications in contact topology like distinguishing contact structures and proving non-fillability.

Contribution

It offers a comprehensive, pedagogical presentation of symplectic field theory, filling gaps in existing literature and illustrating key applications in contact topology.

Findings

Detailed analysis of punctured pseudoholomorphic curves

Methods for distinguishing contact structures

Proofs of symplectic non-fillability

Abstract

This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the opportunity to fill in gaps in the existing literature where necessary, and then gives detailed explanations of a few of the standard applications in contact topology such as distinguishing contact structures up to contactomorphism and proving symplectic non-fillability.