A compendium of pseudoholomorphic beasts in $\mathbb{R}{\times}(S^1{\times}S^2)$

Abstract

This article describes various moduli spaces of pseudoholomorphic curves on the symplectization of a particular overtwisted contact structure on $S^1\times S^2$. 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.