A Note on Finite Dehn Fillings

http://dx.doi.org/10.4153/CMB-1999-017-7
Canad. Math. Bull. 42(1999), 149-154

  Published:1999-06-01
 Printed: Jun 1999

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 $H_1(\partial M)$ 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 $3$.