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Nonzero degree maps between closed orientable three-manifolds
Author(s):
Pierre
Derbez
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3887-3911.
MSC (2000):
Primary 57M50, 51H20
Posted:
March 20, 2007
MathSciNet review:
2302517
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Additional information
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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Additional Information:
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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