Bounds for Kirby-Thompson invariants of knotted surfaces
Geometric Topology
2026-05-13 v1
Abstract
We provide sharp lower bounds for two versions of the Kirby-Thompson invariants for knotted surfaces, one of which was originally defined by Blair, Campisi, Taylor, and Tomova. The second version introduced in this paper measures distances in the dual curve complex instead of the pants complex. We compute the exact values of both KT-invariants for infinitely many knotted surfaces with bridge number at most six.
Keywords
Cite
@article{arxiv.2206.02936,
title = {Bounds for Kirby-Thompson invariants of knotted surfaces},
author = {Román Aranda and Puttipong Pongtanapaisan and Cindy Zhang},
journal= {arXiv preprint arXiv:2206.02936},
year = {2026}
}
Comments
32 pages, 24 figures