Ribbonlength of twisted torus knots

2022/08/07 by Hyoung-Jun Kim, Kim, Hyoungjun, Sungjong No +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #57K10 #57R65 #Biochemical and Structural Characterization #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2208.03676

openalex publication_date 2022/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The ribbonlength Rib(K) of a knot K is the infimum of the ratio of the length of any flat knotted ribbon with core K to its width. A twisted torus knot T_p,q;r,s is obtained from the torus knot T_p,q by twisting r adjacent strands s full twists. In this paper, we show that the ribbonlength of T_p,q;r,s is less then or equal to 2(max \ p, q, r \ +|s|r) where p and q are positive. Furthermore, if r ≤ p-q, then the ribbonlength of T_p,q;r,s is less then or equal to 2(p+(|s|-1)r).

Cited by

• Ribbonlength bounds for pretzel links and knots with ≤ 9 crossings
• Ribbonlength upper bounds for small crossing knots and links
• Bounded ribbonlength for knot families and multi-twist Möbius bands

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• Linear Upper Bound on the Ribbonlength of Torus Knots and Twist Knots
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