Bounding the Kirby-Thompson invariant of spun knots

Abstract

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.

Comments are welcome

References in corpus (4)

• Bridge trisections in ${\mathbb{CP}}^2$ and the Thom conjecture (with Corrigendum)
• Doubly pointed trisection diagrams and surgery on 2-knots
• Kirby-Thompson distance for trisections of knotted surfaces
• Symplectic 4-manifolds admit Weinstein trisections