2005/11/22 by Boileau, Michel, Rubinstein, J. Hyam, Wang, Shicheng
#54M05 #55M25 #57M50 #57N10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.math/0511541
We prove a finiteness result for the ∂-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and ∂-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 S3.