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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 × (S1 × S2) 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 S1 × S2 to appear as the set of |s| limits of the constant s 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