Hierarchies for 3-orbifolds (Q1116120)

A fundamental theorem for the theory of sufficiently large 3-manifolds M, the existence of a hierarchy for M, is generalized to orbifolds: Let Q be a smooth, compact, irreducible, orientable 3-orbifold which is sufficiently large (i.e., it has a 2-sided nonboundary-parallel incompressible 2-suborbifold), contains no bad 2-orbifolds (i.e., every 2-orbifold in Q is covered by a manifold), and in which every 2-sphere with 3 cone points and non-positive (orbifold) Euler characteristic is boundary-parallel. Then Q can be decomposed into orbifold balls by cutting along incompressible 2-orbifolds.