2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60307Let $M$ be a simple 3-manifold with a toral boundary component. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a toroidal manifold, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.3 pagesGeometric Topology57M50text