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arXiv · 2309.03814

Crossing numbers of cable knots

Efstratia Kalfagianni·Rob Mcconkey
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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.

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Efstratia Kalfagianni, Rob Mcconkey. 2024-07-15. Crossing numbers of cable knots. https://doi.org/10.1112/blms.13140

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