Non-zero degree maps between closed orientable three-manifolds

2005/01/09 by Pierre Derbez, P. Derbez, Derbez, P.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Geometric and Algebraic Topology #math.GT #msc:51H20 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0501124

arxiv created 2005/01/09 · arxiv updated 2009/12/01

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.

Related

• Any 3-manifold 1-dominates at most finitely many geometric 3-manifolds
• Finiteness of 3-manifolds associated with non-zero degree mappings
• Non-zero degree maps between 3-manifolds
• Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups
• Finiteness of mapping degrees and \rm PSL(2,\R)-volume on graph manifolds