Crossing numbers of cable knots
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916716158648320 |
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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 |