Geometry & Topology

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

Clifford Henry Taubes

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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.

Article information

Source
Geom. Topol., Volume 10, Number 2 (2006), 785-928.

Dates
Received: 6 April 2004
Accepted: 9 May 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799743

Digital Object Identifier
doi:10.2140/gt.2006.10.785

Mathematical Reviews number (MathSciNet)
MR2240906

Zentralblatt MATH identifier
1134.53045

Subjects
Primary: 53D30: Symplectic structures of moduli spaces
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D05: Symplectic manifolds, general 57R17: Symplectic and contact topology

Keywords
pseudoholomorphic punctured sphere almost complex structure symplectic form moduli space

Citation

Taubes, Clifford Henry. Pseudoholomorphic punctured spheres in $\mathbb{R}{\times}(S^{1}{\times}S^{2})$: Properties and existence. Geom. Topol. 10 (2006), no. 2, 785--928. doi:10.2140/gt.2006.10.785. https://projecteuclid.org/euclid.gt/1513799743


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