Topology Seminar: Liam Watson

The symmetry group of a knot in the three-sphere is the mapping class group of the knot’s exterior. Elements of order two with fixed point set meeting the boundary of the knot exterior are called strong inversions, and a pair (K,h) is called a strongly invertible knot when h is a strong inversion in the symmetry group of K. Studying the equivalence of strongly invertible knots amounts to studying conjugacy classes of strong inversions. I will discuss how to construct invariants of strongly invertible knots using Khovanov homology. Some of this is joint work with Mike Snape and, time permitting, I will also discuss work in progress with Andrew Lobb.