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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2504.13491 |
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| _version_ | 1866909584138960896 |
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| author | Ito, Tetsuya |
| author_facet | Ito, Tetsuya |
| contents | Cromwell proved that the minimum $v$-degree of the HOMFLY polynomial of homogeneous link $L$ is bounded above by $1-χ(L)$, where $χ(L)$ is the maximum Euler characteristic of Seifert surfaces of $L$. We prove its slice version, stating that the minimum $v$-degree of the HOMFLY polynomial of homogeneous link $L$ is bounded above by $1-χ_4(L)$, the maximum 4-dimensional Euler characteristic of $L$. As a byproduct, we prove a conjecture of Stoimenow that for an alternating link, the minimum $v$-degree of the HOMFLY polynomial is smaller than or equal to its signature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A slice Cromwell inequality of homogeneous links Ito, Tetsuya Geometric Topology Cromwell proved that the minimum $v$-degree of the HOMFLY polynomial of homogeneous link $L$ is bounded above by $1-χ(L)$, where $χ(L)$ is the maximum Euler characteristic of Seifert surfaces of $L$. We prove its slice version, stating that the minimum $v$-degree of the HOMFLY polynomial of homogeneous link $L$ is bounded above by $1-χ_4(L)$, the maximum 4-dimensional Euler characteristic of $L$. As a byproduct, we prove a conjecture of Stoimenow that for an alternating link, the minimum $v$-degree of the HOMFLY polynomial is smaller than or equal to its signature. |
| title | A slice Cromwell inequality of homogeneous links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2504.13491 |