Lectures on Symplectic Field Theory

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.

343pp; the final three chapters are missing from this manuscript but will be included in the published version, which is to appear in the EMS Lectures in Mathematics series; a few minor errors corrected in v2; comments and corrections welcome

References in corpus (6)

• Compactness results in Symplectic Field Theory
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Weak Symplectic Fillings and Holomorphic Curves
• Vanishing of the contact homology of overtwisted contact 3--manifolds
• Kuranishi atlases with trivial isotropy - the 2013 state of affairs

Cited by in corpus (24)

• Contact homology and virtual fundamental cycles
• Proof of the simplicity conjecture
• Automatic transversality in contact homology II: filtrations and computations
• Algebraic Torsion in higher-dimensional contact manifolds
• Castelnuovo's bound and rigidity in almost complex geometry
• On cobordism maps on periodic Floer homology
• Symplectic capacities, unperturbed curves, and convex toric domains
• Fiber Floer cohomology and conormal stops
• Categorical mirror symmetry on cohomology for a complex genus 2 curve
• Lectures on Polyfolds and Symplectic Field Theory
• On the embedding complexity of Liouville manifolds
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• Embedded contact homology of prequantization bundles
• Polyfold and SFT Notes II: Local-Local M-Polyfold Constructions
• On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
• S^1-equivariant contact homology for hypertight contact forms
• Polyfold and SFT Notes I: A Primer on Polyfolds and Construction Tools
• Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves
• The $L_{\infty }$-structure on symplectic cohomology
• An Index Formula for Cauchy-Riemann Operators on Surfaces with Boundary Punctures
• Essential tori in spaces of symplectic embeddings
• 5-dimensional Bourgeois contact structures are tight
• Homological invariants of codimension 2 contact submanifolds
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology