  The 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.

Symplectic Geometry;Geometric Topology