2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221911This 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.This is the version published by Geometry & Topology on 24 July 2006Symplectic GeometryGeometric Topology53D30, 53C15, 53D05, 57R17text