Abstract:

A knot is said to be slice if it bounds a smoothly embedded disc in B^4. For a long time, the question of sliceness had been answered for all knots with up to 12 crossings – except the Conway knot. Earlier this year, Lisa Piccirillo published a proof that the Conway knot is not slice, using relatively basic tools from low-dimensional topology and knot theory. I will explain how she used Kirby calculus to construct another knot sharing a trace (a 4-manifold that can be built from a knot via handle attachment) with the Conway knot. Time permitting, I will outline how Rasmussen’s s-invariant can then be used to show that Piccirillo’s knot (and hence the Conway knot) is not slice.