Non-zero degree maps between closed orientable three-manifolds
Geometric Topology
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0501124,
title = {Non-zero degree maps between closed orientable three-manifolds},
author = {P. Derbez},
journal= {arXiv preprint arXiv:math/0501124},
year = {2007}
}