Characterising slopes for knots of hyperbolic type

  • Laura Wakelin (MPI for Mathematics)
E2 10 (Leon-Lichtenstein)


A slope p/q is characterising for a knot K in the 3-sphere if the oriented homeomorphism type of the manifold obtained by performing Dehn surgery of slope p/q on K uniquely determines the knot K. Sorya showed that for any knot K, there exists a constant C(K) such that any slope p/q with |q|≥C(K) is characterising for K. However, the proof of the existence of C(K) in the general case is non-constructive, which naturally evokes the question of how to compute explicit values for C(K). In this talk, I will explore methods for finding C(K) in the case where K is a knot of hyperbolic type (meaning that the JSJ decomposition of its complement has a hyperbolic outermost JSJ piece). I will begin with the simplest case, in which K is a hyperbolic knot; time permitting, I will also discuss some ongoing joint work with Patricia Sorya on the more general case.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar