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

Taubes, Clifford Henry

doi:10.2140/gt.2006.10.785

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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

DOI: 10.2140/gt.2006.10.785

arXiv: 0903.0142

Abstract

This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in $ℝ \times (S^{1} \times S^{2})$ 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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 53D30

Secondary: 53C15, 53D05, 57R17

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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

Volume 10, issue 2 (2006)