Abbas C. An Introduction to Compactness Results in Symplectic Field Theory

Springer, 2014. — 257 p. — ISBN: 3642315429.This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade.Riemann Surfaces
Smooth and Noded Riemann Surfaces
Riemann Surfaces and Hyperbolic Geometry
The Deligne–Mumford Compactness Result
Pseudoholomorphic Curves
Basic Definitions
Asymptotic Behavior Near a Puncture
Isoperimetric Inequality, Monotonicity Lemma, Removal of Singularities
Finite-Energy Strips and Cylinders of Small Area
The SFT Compactness Results
Holomorphic Buildings for Curves Without Boundary
Adding Additional Marked Points
The Compactness Result for the Case Without Boundary
More General Holomorphic Buildings and Compactness Results