2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73037The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work of Gromov, McDuff and Taubes on symplectic 4-manifolds concerning pseudoholomorphic curves and Seiberg-Witten theory. They form the technical backbone of the proof that a symplectic s-cobordism of elliptic 3-manifolds (with a canonical contact structure on the boundary) is smoothly a product. One interesting feature of the theory is that existence of pseudoholomorphic curves gives certain restrictions on the singular points of the 4-orbifold contained by the pseudoholomorphic curves. In the last section, we discuss applications (or potential ones) of the theory in some other problems such as symplectic finite group actions on 4-manifolds, symplectic circle actions on 6-manifolds, and algebraic surfaces with quotient singularities.27 pages, no figures, expository article, improved exposition, accepted for publication in Proceedings of Conference on Geometry and Topology of Manifolds, McMaster University, May 14-18, 2004Symplectic GeometryGeometric Topology57R17, 57R57, 57M60text