Event Details

Speaker: Laura Wakelin (KCL) Title: Effective bounds on characterising slopes for all knots

Abstract: Dehn surgery is a process by which a knot K in the 3-sphere, together with a rational number p/q called a slope, can be used to build a new 3-manifold. 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. In this talk, I will give an overview of joint work with Patricia Sorya in which we determine, for any given knot K, an explicit bound C(K) such that |q|>C(K) implies that p/q is a characterising slope for K. Moreover, we show that in some cases our value for C(K) is optimal.