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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonzero degree maps between closed orientable three-manifolds


Author: Pierre Derbez
Journal: Trans. Amer. Math. Soc. 359 (2007), 3887-3911
MSC (2000): Primary 57M50, 51H20
Published electronically: March 20, 2007
MathSciNet review: 2302517
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Abstract: This paper adresses the following problem: Given a closed orientable three-manifold $ M$, are there at most finitely many closed orientable three-manifolds 1-dominated by $ M$? We solve this question for the class of closed orientable graph manifolds. More precisely the main result of this paper asserts that any closed orientable graph manifold 1-dominates at most finitely many orientable closed three-manifolds satisfying the Poincaré-Thurston Geometrization Conjecture. To prove this result we state a more general theorem for Haken manifolds which says that any closed orientable three-manifold $ M$ 1-dominates at most finitely many Haken manifolds whose Gromov simplicial volume is sufficiently close to that of $ M$.


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Pierre Derbez
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, UMR 6632, Centre de Mathéma- tiques et d’Informatique, Université Aix-Marseille I, Technopole de Chateau-Gombert, 39, rue Frédéric Joliot-Curie - 13453 Marseille Cedex 13, France
Email: derbez@cmi.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04130-X
PII: S 0002-9947(07)04130-X
Keywords: Haken manifold, Seifert fibered space, geometric 3-manifold, graph manifold, Gromov simplicial volume, nonzero degree maps, Dehn filling
Received by editor(s): March 21, 2005
Received by editor(s) in revised form: July 18, 2005
Published electronically: March 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.