Roots of torsion polynomials and dominations

Abstract

We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3-manifold M are contained in a compact part of the complex plane a priori determined by M. This result is applied to prove that when M is closed, it dominates at most finitely many Sol manifolds.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

Finiteness of nonzero degree maps between 3‐manifolds

“…Theorem 2.1 [3,Corollary 3.6]. Every orientable closed 3-manifold dominates at most finitely many homeomorphically distinct 3-manifolds which are Sol-geometric.…”

“…Moreover, the finiteness of Sol-geometric targets under domination has been proved in [BBW]: BBW,Corollary 3.6]). Every orientable closed 3-manifold dominates at most finitely many distinct Sol-geometric 3-manifolds.…”