Pseudoholomorphic punctured spheres in R×(S¹×S²): Properties and existence

Taubes, Clifford Henry¹

¹ Department of Mathematics, Harvard University, Cambridge MA 02138, USA

Geometry & topology, Tome 10 (2006) no. 2, pp. 785-928.

Résumé

This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in $ℝ\times \left(S^1\times S^2\right)$ as defined by a certain natural pair of almost complex structure and symplectic form. This article proves that all moduli space components are smooth manifolds. Necessary and sufficient conditions are also given for a collection of closed curves in $S^1\times S^2$ to appear as the set of $|s|\to \infty$ limits of the constant $s\in ℝ$ slices of a pseudoholomorphic, multiply punctured sphere.

Détail

DOI : 10.2140/gt.2006.10.785

Keywords: pseudoholomorphic, punctured sphere, almost complex structure, symplectic form, moduli space

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