JournalscmhVol. 89, No. 1pp. 33–68

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

  • Michel Boileau

    Université Paul Sabatier, Toulouse, France
  • J. Hyam Rubinstein

    University of Melbourne, Parkville, Australia
  • Shicheng Wang

    Peking University, Beijing, China
Finiteness of 3-manifolds associated with non-zero degree  mappings cover
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Abstract

We prove a finiteness result for the \partial-patterned guts decomposition of all 33-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 orientable 3-manifold dominates only finitely many exteriors of knots in S3S^3.

Cite this article

Michel Boileau, J. Hyam Rubinstein, Shicheng Wang, Finiteness of 3-manifolds associated with non-zero degree mappings. Comment. Math. Helv. 89 (2014), no. 1, pp. 33–68

DOI 10.4171/CMH/312