Open 3-manifolds whose fundamental groups have infinite center, and a torus theorem for 3-orbifolds

Our main result is a characterization of open Seifert fibered 3 3 -manifolds in terms of the fundamental group and large-scale geometric properties of a triangulation. As an application, we extend the Seifert Fiber Space Theorem and the Torus Theorem to a class of 3 3 -orbifolds.