Crossing numbers of cable knots

Fuente: arXiv
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Bibliographic Details
Main Authors: Kalfagianni, Efstratia, Mcconkey, Rob
Format: Preprint
Published: 2023
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author Kalfagianni, Efstratia
Mcconkey, Rob
author_facet Kalfagianni, Efstratia
Mcconkey, Rob
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2309_03814
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Crossing numbers of cable knots
Kalfagianni, Efstratia
Mcconkey, Rob
Geometric Topology
57K10, 57K14, 57K16
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.
title Crossing numbers of cable knots
topic Geometric Topology
57K10, 57K14, 57K16
url https://arxiv.org/abs/2309.03814