Hello everyone,

Today we have Dave Futer speaking in the seminar:

He will be speaking on some cool stuff and his title and abstract are below:

Title: Systoles and cosmetic surgeries

Abstract: A pair of distinct slopes for a knot K is called a cosmetic surgery pair if the Dehn surgeries along those slopes yield the same oriented 3-manifold. Gordon conjectured that such pairs do not exist. 

I will describe a theorem that says any potential cosmetic surgery pairs on a hyperbolic knot K belong to a finite list of slopes, whose size is determined by the systole (shortest closed geodesic) in the complement of K. For a typical knot, this list has no more than 10 pairs of slopes. This makes it feasible to check the remaining pairs by computer and prove that K has no cosmetic surgeries at all. For instance, prime knots up to 15 crossings have no cosmetic surgeries. This is joint work with Jessica Purcell and Saul Schleimer.