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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.13491 |
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Table of 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.