On the arc index and Turaev genus of a link

Álvaro Del Valle Vílchez; Adam M. Lowrance

doi:10.1007/s13398-026-01856-y

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arXiv · 2509.21274

On the arc index and Turaev genus of a link

Álvaro Del Valle Vílchez·Adam M. Lowrance

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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.

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BibTeX RIS

Álvaro Del Valle Vílchez, Adam M. Lowrance. 2025-09-25. On the arc index and Turaev genus of a link. https://doi.org/10.1007/s13398-026-01856-y

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