电缆结的交叉数量

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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摘要

我们利用彩色琼斯结多项式的度数来证明，具有交叉数 c $c$ 的适当结的 ( p , q ) $(p,q)$ 电缆的交叉数大于 q 2 c $q^2\, c$ 。作为应用，我们确定了适当结的 2 个缆线的交叉数。我们还确定了任何适当结与适当结的 2-cable 的连接和的交叉数。

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Crossing numbers of cable knots

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.