Characterizing slopes for torus knots and hyperbolic knots

Abstract: A slope $p/q$ is a characterizing slope for a knot $K$ in the $3$-sphere if the oriented homeomorphism type of $p/q$-surgery on $K$ determines $K$ uniquely. It is known that for a given torus knot all but finitely many non-integer slopes are characterizing and that for hyperbolic knots all but finitely many slopes with $q>2$ are characterizing. I will discuss the proofs of these results, which have a surprising amount in common.

group theorygeometric topologymetric geometry

Audience: researchers in the topic

McGill geometric group theory seminar