On the arc index and Turaev genus of a link

2025/09/25 by Vílchez, Álvaro Del Valle, Lowrance, Adam M.
#57K18 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57K10 #Secondary 20F36

paper · doi:10.48550/arxiv.2509.21274

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.

Citations

• Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14
• Minimal grid diagrams of the prime alternating knots with 13 crossings
• Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13
• Near extremal Khovanov homology of Turaev genus one links
• Jones diameter and crossing number of knots
• Legendrian Torus and Cable Links
• Minimal Grid Diagrams of the Prime Alternating Knots with 12 Crossings
• Concordance invariants and the Turaev genus
• Torsion in thin regions of Khovanov homology
• Homotopy type of circle graphs complexes motivated by extreme Khovanov\n homology
• A geometric description of the extreme Khovanov cohomology
• Link diagrams with low Turaev genus
• Closures of positive braids and the Morton-Franks-Williams inequality
• Prime knots whose arc index is smaller than the crossing number
• Prime knots with arc index up to 11 and an upper bound of arc index for\n non-alternating knots
• The dealternating number and the alternation number of a closed 3-braid
• Maximal Thurston-Bennequin number of +adequate links
• Extreme coefficients of Jones polynomials and graph theory
• The spread and extreme terms of Jones polynomials
• ALGORITHMS FOR POSITIVE BRAIDS

Cited by

• A characterization of adequate Turaev genus one links

Related

• A note on closed 3-braids
• The Braid Index Of Reduced Alternating Links
• Invariants for Turaev genus one links
• A characterization of adequate Turaev genus one links
• Signature and crossing number of links