A note on finite Dehn fillings

Let M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if the minimal Culler-Shalen norm of a non-zero class in H₁ (∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yield manifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.