Bounding the Kirby-Thompson invariant of spun knots
Geometric Topology
2026-05-13 v1
Abstract
A bridge trisection of a smooth surface in is a decomposition analogous to a bridge splitting of a link in . 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.
Cite
@article{arxiv.2112.02420,
title = {Bounding the Kirby-Thompson invariant of spun knots},
author = {Román Aranda and Puttipong Pongtanapaisan and Scott A. Taylor and Cindy Zhang},
journal= {arXiv preprint arXiv:2112.02420},
year = {2026}
}
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