Bounding the Kirby-Thompson invariant of spun knots

Román Aranda; Puttipong Pongtanapaisan; Scott A. Taylor; Cindy Zhang

doi:10.2140/agt.2024.24.3363

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arXiv · 2112.02420

Bounding the Kirby-Thompson invariant of spun knots

Román Aranda·Puttipong Pongtanapaisan·Scott A. Taylor·Cindy Zhang

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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.

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Román Aranda, Puttipong Pongtanapaisan, Scott A. Taylor, Cindy Zhang. 2021-12-04. Bounding the Kirby-Thompson invariant of spun knots. https://doi.org/10.2140/agt.2024.24.3363

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