Bounding the Kirby-Thompson invariant of spun knots

A bridge trisection of a smooth surface in $S^4$ is a decomposition analogous to a bridge splitting of a link in $S^3$. The Kirby-Thompson invariant of a bridge trisection measures its complexity in terms of distances between disc sets in the pants complex of the trisection surface. We give the first significant bounds for the Kirby-Thompson invariant of spun knots. In particular, we show that the Kirby-Thompson invariant of the spun trefoil is 15.