#### Volume 10, issue 2 (2006)

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Pseudoholomorphic punctured spheres in $\mathbb{R}{\times}(S^{1}{\times}S^{2})$: Properties and existence

### Clifford Henry Taubes

Geometry & Topology 10 (2006) 785–928
 arXiv: 0903.0142
##### Abstract

This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in $ℝ×\left({S}^{1}×{S}^{2}\right)$ 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 ${S}^{1}×{S}^{2}$ to appear as the set of $|s|\to \infty$ limits of the constant $s\in ℝ$ slices of a pseudoholomorphic, multiply punctured sphere.

##### Keywords
pseudoholomorphic, punctured sphere, almost complex structure, symplectic form, moduli space
##### Mathematical Subject Classification 2000
Primary: 53D30
Secondary: 53C15, 53D05, 57R17
##### Publication
Received: 6 April 2004
Accepted: 9 May 2006
Published: 24 July 2006
Proposed: Rob Kirby
Seconded: Peter Ozsváth, Yasha Eliashberg
##### Authors
 Clifford Henry Taubes Department of Mathematics Harvard University Cambridge MA 02138 USA