Geometry & Topology, Vol. 6 (2002) Paper no. 23, pages 657--814.

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

Clifford Henry Taubes

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.

Keywords. Pseudoholomorphic curves, moduli spaces, contact structures

AMS subject classification. Primary: 32Q65. Secondary: 57R17, 57R57.

DOI: 10.2140/gt.2002.6.657

E-print: arXiv:math.GT/0212389

Submitted to GT on 21 November 2002. Paper accepted 18 December 2002. Paper published 18 December 2002.

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Clifford Henry Taubes
Department of Mathematics, Harvard University
Cambridge, MA 02138, USA
Email: chtaubes@math.harvard.edu

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