Slicing degree of knots
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910421747761152 |
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| author | Qin, Qianhe |
| author_facet | Qin, Qianhe |
| contents | The slicing degree of a knot $K$ is defined as the smallest integer $k$ such that $K$ is $k$-slice in $\#^n \overline{\mathbb{CP}^2}$ for some $n$. In this paper, we establish bounds for the slicing degrees of knots using Rasmussen's $s$-invariant, knot Floer homology and singular instanton homology. We compute the slicing degrees for many small knots (with crossing numbers up to $9$) and for some families of torus knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slicing degree of knots Qin, Qianhe Geometric Topology 57K10, 57K18, 57K40 The slicing degree of a knot $K$ is defined as the smallest integer $k$ such that $K$ is $k$-slice in $\#^n \overline{\mathbb{CP}^2}$ for some $n$. In this paper, we establish bounds for the slicing degrees of knots using Rasmussen's $s$-invariant, knot Floer homology and singular instanton homology. We compute the slicing degrees for many small knots (with crossing numbers up to $9$) and for some families of torus knots. |
| title | Slicing degree of knots |
| topic | Geometric Topology 57K10, 57K18, 57K40 |
| url | https://arxiv.org/abs/2404.15991 |