Non-zero degree maps between closed orientable three-manifolds

Details Non-zero degree maps between closed orientable three-manifolds Non-zero degree maps between closed orientable three-manifolds

2005-01-09

arxiv.org/abs/math/0501124v1

Mathematics

Geometric Topology

Scientific paper

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 presisely 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 Poincare-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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