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Laura Wakelin : Finding characterising slopes for all knots

A slope p/q is characterising for a knot K if the oriented homeomorphism type of the 3-manifold obtained by performing Dehn surgery of slope p/q on K uniquely determines the knot K. For any knot K, there exists a bound C(K) such that any slope p/q with |q|â?¥C(K) is characterising for K. This bound has previously been constructed for certain classes of knots, including torus knots, hyperbolic knots and composite knots. In this talk, I will give an overview of joint work with Patricia Sorya in which we complete this realisation problem for all remaining knots.

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