Non-zero Degree Maps between Closed Orientable Three-manifolds
نویسنده
چکیده
This paper adresses the following problem: Given a closed orientable threemanifold 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 presisely the main result of this paper asserts that any closed orientable graph manifold 1dominates at most finitely many orientable closed three-manifolds satisfying the PoincaréThurston 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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