Let M be a one-cusped hyperbolic 3-manifold. A slope on the boundary of the compact core of M is called exceptional if the corresponding Dehn filling produces a non-hyperbolic manifold. We give new upper bounds for the distance between two exceptional slopes˛andˇin several situations. These include cases where M.ˇ/ is reducible and where M.˛/ has finite 1 , or M.˛/ is very small, or M.˛/ admits a 1 -injective immersed torus. 57M25, 57M50, 57M99

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