Finiteness of 3-manifolds associated with non-zero degree mappings

We prove a finiteness result for the partial derivative-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and partial derivative-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a given compact 3-manifold belong, up to homeomorphism, to a finite collection of compact 3-manifolds. We show also that any closed orientable 3-manifold dominates only finitely many integral homology spheres and any compact orientable 3-manifold dominates only finitely many exteriors of knots in S-3.MathematicsSCI(E)0ARTICLEboileau@math.univ-toulouse.fr; rubin@ms.unimelb.edu.au; wangsc@math.pku.edu.cn133-688