Toroidal Dehn filling on large hyperbolic 3-manifolds (Q851504)

Let \(M\) be a compact orientable 3-manifold with a torus boundary component \(T_0\). For a slope \(\gamma\) denote by \(M(\gamma)\) the manifold obtained by \(\gamma\)-Dehn filling on \(M\). The main result of the paper states the following. Let \(M\) be a hyperbolic 3-manifold whose boundary is a single torus \(T_0\). If there are two toroidal slopes \(\alpha\) and \(\beta\) on \(T_0\) at distance 5, then \(M\) is a \(\mathbb Q\)-homology solid torus. Moreover, either \(M(\alpha)\) or \(M(\beta)\) contains an essential torus which meets the core of the attached solid torus minimally in at most two points. As a corollary, the following result is obtained. Let \(M\) be a large hyperbolic 3-manifold with a torus boundary component \(T_0\). If \(M\) admits two toroidal Dehn fillings with slopes \(\alpha\) and \(\beta\) on \(T_0\), then the distance between these slopes is at most 4.