On the arc index and Turaev genus of a link
Geometric Topology
2026-05-12 v2
Abstract
We compute the arc index of an adequate link and establish bounds on the arc index of the closure of a positive 3-braid. We also conjecture an inequality between the crossing number, arc index, and Turaev genus of a link and show the conjecture is true for several infinite families of links including alternating links, links with Turaev genus one, adequate links, closures of positive 3-braids, torus links, and most Kanenobu knots.
Cite
@article{arxiv.2509.21274,
title = {On the arc index and Turaev genus of a link},
author = {Álvaro Del Valle Vílchez and Adam M. Lowrance},
journal= {arXiv preprint arXiv:2509.21274},
year = {2026}
}
Comments
33 pages, 19 figures