Bounding the Kirby-Thompson invariant of spun knots (Q6632134)

A basic context of the paper is to develop 2-knot or 4-manifold invariants using trisections. A \textit{bridge trisection} of a smooth surface in \(S^4\) is a decomposition analogous to a bridge splitting of a classical link in \(S^3\) and gives rise to the fundamental notion of the \textit{bridge number} of a knotted smooth surface in \(S^4\). \textit{R. Kirby} and \textit{A. Thompson} [Proc. Natl. Acad. Sci. USA 115, No. 43, 10857--10860 (2018; Zbl 1421.57031)] defined an invariant of a bridge trisection which measures its complexity in terms of distances between disk sets in the pants complex of the trisection surface. ``We give the first significant bound for the Kirby-Thompson invariant of spun knots. In particular, we show that the Kirby-Thompson invariant of the spun trefoil is 15.''