Abstract
Myers shows that every compact, connected, orientable 3 3 -manifold with no 2 2 -sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 3 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.
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