English

Bounding the Kirby-Thompson invariant of spun knots

Geometric Topology 2026-05-13 v1

Abstract

A bridge trisection of a smooth surface in S4S^4 is a decomposition analogous to a bridge splitting of a link in S3S^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.

Keywords

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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