Transactions of the American Mathematical Society

Author(s): Pierre Derbez
Journal: Trans. Amer. Math. Soc. 359 (2007), 3887-3911.
MSC (2000): Primary 57M50, 51H20
Posted: March 20, 2007
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Abstract: This paper adresses the following problem: Given a closed orientable three-manifold

, are there at most finitely many closed orientable three-manifolds 1-dominated by

? 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

1-dominates at most finitely many Haken manifolds whose Gromov simplicial volume is sufficiently close to that of

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57M50, 51H20

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: 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
Posted: March 20, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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