Geometry & Topology

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

Clifford Henry Taubes

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

pseudoholomorphic punctured sphere almost complex structure symplectic form moduli space


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.

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