Toroidal and annular Dehn fillings

Cameron McA. Gordon; Ying-Qing Wu

paper

Toroidal and annular Dehn fillings

arXiv:math/9705221

Abstract

Suppose $M$ is a hyperbolic 3-manifold which admits two Dehn fillings $M (r_{1})$ and $M (r_{2})$ such that $M (r_{1})$ contains an essential torus and $M (r_{2})$ contains an essential annulus. It is known that $Δ = Δ (r_{1}, r_{2}) \leq 5$ . We will show that if $Δ = 5$ then $M$ is the Whitehead sister link exterior, and if $Δ = 4$ then $M$ is the exterior of either the Whitehead link or the 2-bridge link associated to the rational number $3/10$ . There are infinitely many examples with $Δ = 3$ .