Crossing numbers of cable knots

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-08-26 DOI:10.1112/blms.13140

Efstratia Kalfagianni, Rob Mcconkey

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引用次数: 0

Abstract

We use the degree of the colored Jones knot polynomials to show that the crossing number of a $(p, q)$ -cable of an adequate knot with crossing number $c$ is larger than $q^{2} c$ . As an application, we determine the crossing number of 2-cables of adequate knots. We also determine the crossing number of the connected sum of any adequate knot with a 2-cable of an adequate knot.