P2-reducing and toroidal Dehn fillings

Abstract

Let M be a compact, connected, orientable 3-manifold with a torus boundary component $\partial_{0}M$. A slope on $\partial_{0}M$ is the isotopy class of an unoriented essential simple loop. For a slope r, the manifold obtained from M by r-Dehn filling is M(r) = M$\cup$Vr, where Vr is a solid torus glued to M along $\partial_{0}M$ in such a way that r bounds a meridian disc in Vr. If r and s are two slopes on $\partial_{0}M$, then $\Delta$(r, s) denotes their minimal geometric intersection number.