TOROIDAL AND ANNULAR DEHN FILLINGS

CAMERON MCA. GORDON YING-QING WU

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}) ≤ 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.