Tangle replacements and knot Floer homology torsions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916442721484800 |
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| author | Eftekhary, Eaman |
| author_facet | Eftekhary, Eaman |
| contents | We show that the torsion order $\mathrm{Ord}(K)$ of a knot $K$ in knot Floer homology gives a lower bound on the minimum number $n$ such that an oriented $(n+1)$-tangle replacement unknots $K$. This generalizes earlier results by Alishahi and the author and by Juhasz, Miller and Zemke, that $\mathrm{Ord}(K)$ is a lower bound for both the unknotting number $u(K)$ and for $br(K)-1$, where $br(K)$ denotes the bridge index of $K$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_13283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tangle replacements and knot Floer homology torsions Eftekhary, Eaman Geometric Topology We show that the torsion order $\mathrm{Ord}(K)$ of a knot $K$ in knot Floer homology gives a lower bound on the minimum number $n$ such that an oriented $(n+1)$-tangle replacement unknots $K$. This generalizes earlier results by Alishahi and the author and by Juhasz, Miller and Zemke, that $\mathrm{Ord}(K)$ is a lower bound for both the unknotting number $u(K)$ and for $br(K)-1$, where $br(K)$ denotes the bridge index of $K$. |
| title | Tangle replacements and knot Floer homology torsions |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2410.13283 |