Celebratio Mathematica — Rubinstein

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Works connected to Michel Charles Boileau

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M. Boileau, J. H. Rubinstein, and S. Wang: Finiteness of 3-manifolds associated with non zero degree mappings. Preprint, 2005. ArXiv 0511541 techreport

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 \( \mathbb{S}^3 \).

Shicheng Wang	Related
Michel Charles Boileau	Related