Dehn fillings and small surfaces

Abstract

Let M be a compact, connencted, orientable, hyperbolic 3-manifold with a toral boundary component. First, we find the maximal distance between $P^2 -reducing$ and toroidal Dehn fillings. Then we give a very short proof of the result obtained independently by Oh and Wu. Finally we investigate the situations that one filling creates a reducing sphere, and the other creates an essential small surfaces such as a sphere, torus or annulus.