Linear Bounds of the Crosscap Number of Knots
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908627131957248 |
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| author | McConkey, Rob |
| author_facet | McConkey, Rob |
| contents | Kalfagianni and Lee found two-sided bounds for the crosscap number of an alternating link in terms of certain coefficients of the Jones polynomial. We show here that we can find similar two-sided bounds for the crosscap number of Conway sums of strongly alternating tangles. Then we find families of links for which these coefficients of the Jones polynomial and the crosscap number grow independently. These families will enable us to show that neither linear bound generalizes for all links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear Bounds of the Crosscap Number of Knots McConkey, Rob Geometric Topology Kalfagianni and Lee found two-sided bounds for the crosscap number of an alternating link in terms of certain coefficients of the Jones polynomial. We show here that we can find similar two-sided bounds for the crosscap number of Conway sums of strongly alternating tangles. Then we find families of links for which these coefficients of the Jones polynomial and the crosscap number grow independently. These families will enable us to show that neither linear bound generalizes for all links. |
| title | Linear Bounds of the Crosscap Number of Knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2308.09159 |