Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Properties and existence

Abstract

This is the first of at least two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R x (S^1 x 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 x S^2 to appear as the set of |s| --> infinity limits of the constant s in R slices of a pseudoholomorphic, multiply punctured sphere.

arXiv commentThis is the version published by Geometry & Topology on 24 July 2006

References in corpus (5)

• Compactness results in Symplectic Field Theory
• The periodic Floer homology of a Dehn twist
• Constructing symplectic forms on 4-manifolds which vanish on circles
• The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on S^1 X B^3
• A compendium of pseudoholomorphic beasts in R x (S^1 x S^2)

Cited by in corpus (7)

• The periodic Floer homology of a Dehn twist
• Constructing Lefschetz-type fibrations on four-manifolds
• Beyond ECH capacities
• HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence
• Taming the pseudoholomorphic beasts in $\mathbb{R}\times (S^1\times S^2)$
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Moduli space parametrizations
• Pseudo-holomorphic maps into folded symplectic four-manifolds