The classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori

Abstract

Let K=K(w,b,t) be a 1-bridge braid in a solid torus V, and let γ be a (p,q) curve on the torus T=∂V of the exterior MK of K. It will be shown that Dehn filling on T along γ produces a solid torus if and only if p and q satisfy one of four conditions determined by the parameters (w,b,t) of the knot K. This solves the classification problem raised by Menasco and Zhang for such Dehn fillings.