A compendium of pseudoholomorphic beasts in R x (S^1 x S^2)

Abstract

This article describes various moduli spaces of pseudoholomorphic curves on the symplectization of a particular overtwisted contact structure on S^1 x S^2. This contact structure appears when one considers a closed self dual form on a 4-manifold as a symplectic form on the complement of its zero locus. The article is focussed mainly on disks, cylinders and three-holed spheres, but it also supplies groundwork for a description of moduli spaces of curves with more punctures and non-zero genus.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper23.abs.html

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• Embedded contact homology and open book decompositions
• HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Properties and existence
• Sutured ECH is a natural invariant
• Taming the pseudoholomorphic beasts in $\mathbb{R}\times (S^1\times S^2)$
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Moduli space parametrizations
• Pseudo-holomorphic maps into folded symplectic four-manifolds