Effective bounds on characterizing slopes for all knots

Abstract: A slope p/q is characterizing for knot K if the resulting Dehn surgery determines K up to isotopy. Generalizing a question of Baker and Motegi, McCoy conjectured that for any knot, non-integral slopes p/q with |p|+|q| sufficiently large are characterizing. An advance towards this conjecture is the existence, for any knot K, of a bound C(K) such that any slope p/q with |q|>C(K) is characterizing for K. In this talk, based on joint work with Laura Wakelin, I explain how to explicitely construct such a bound C(K) for any knot.