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

Abstract

We prove a finiteness result for the $\partial$-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and $\partial$-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 3-manifolds orientable 3-manifold dominates only finitely many exterior of knots in $S^3$.

34 pages, 5 figures

References in corpus (2)

• Roots of torsion polynomials and dominations
• Multicomplexes, bounded cohomology and additivity of simplicial volume

Cited by in corpus (3)

• Epimorphisms between 2-bridge link groups
• Epimorphisms and Boundary Slopes of 2-Bridge Knots
• Simon's conjecture for fibered knots