Exceptional surgeries in 3-manifolds

Abstract

Myers shows that every compact, connected, orientable $3$--manifold with no $2$--sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every $3$--manifold subject to the above conditions contains a hyperbolic knot which admits a non-trivial non-hyperbolic surgery, a toroidal surgery in particular. We conclude with a question and a conjecture about reducible surgeries.

5 pages, 3 figures, version 2 is supported by ancillary files which include certificates of computations done in sage. There are minor changes to the exposition to reference these files