Communications in Analysis and Geometry
Volume 12 (2004)
Non-integral Toroidal Dehn Surgeries
Pages: 417 – 485
If we perform a non-trivial Dehn surgery on a hyperbolic knot in the 3- sphere, the result is usually a hyperbolic 3-manifold. However, there are exceptions: there are hyperbolic knots with surgeries that give lens spaces , small Seifert fiber spaces , , , , and toroidal manifolds, that is, manifolds containing (embedded) incompressible tori , . In particular, Eudave-Muñoz  has explicitly described an infinite family of hyperbolic knots k(, m, n, p), each of which has a specific half-integral toroidal surgery. (These are the only known examples of non-trivial, non-integral, non-hyperbolic surgeries on hyperbolic knots.) Here we show that these knots are the only hyperbolic knots with non-integral toroidal surgeries.