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

Clifford Henry Taubes

Geometry & Topology 6 (2002) 657–814

arXiv: math.GT/0212389

Abstract

This article describes various moduli spaces of pseudoholomorphic curves on the symplectization of a particular overtwisted contact structure on S1 × S2. 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.

Keywords
pseudoholomorphic curves, moduli spaces, contact structures
Mathematical Subject Classification 2000
Primary: 32Q65
Secondary: 57R17, 57R57
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Publication
Received: 21 November 2002
Accepted: 18 December 2002
Published: 18 December 2002
Proposed: Robion Kirby
Seconded: Yasha Eliashberg, John Morgan
Authors
Clifford Henry Taubes
Department of Mathematics
Harvard University
Cambridge
Massachusetts 02138
USA