Nonzero degree maps between closed orientable three-manifolds

• Autores: Pierre Derbez
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 8, 2007, págs. 3887-3911
• Idioma: inglés
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• Resumen

  • 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 M1-dominates at most finitely many Haken manifolds whose Gromov simplicial volume is sufficiently close to that of M.