Title: Characterizing  slopes  for  hyperbolic  and  torus  knots
Speaker:  Duncan McCoy, University of Texas
Date: Dec 4, 2018
Time: 2:30 PM
Room: MSCS 405
Abstract: Given a knot $K$ in $S^3$, we say that $p/q$ is a characterizing slope if the oriented homeomorphism type of $p/q$-surgery on $K$ is sufficient to uniquely determine the knot $K$. 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 both results, which have a surprising amount in common.