Effective bounds on characterising slopes for all knots
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908628634566656 |
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| author | Sorya, Patricia Wakelin, Laura |
| author_facet | Sorya, Patricia Wakelin, Laura |
| contents | A slope $p/q$ is characterising for a knot $K \subset \mathbb{S}^3$ if the orientation-preserving homeomorphism type of the manifold $\mathbb{S}^3_K(p/q)$ obtained by performing Dehn surgery of slope $p/q$ along $K$ uniquely determines the knot $K$. We combine new applications of results from hyperbolic geometry with previous individual work of the authors to determine, for any given knot $K$, an explicit bound $\mathcal{C}(K)$ such that $|q| > \mathcal{C}(K)$ implies that $p/q$ is a characterising slope for $K$. Furthermore, we find an optimal such $\mathcal{C}(K)$ for certain satellite knots with winding number zero patterns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective bounds on characterising slopes for all knots Sorya, Patricia Wakelin, Laura Geometric Topology 57K10 (Primary), 57K30, 57K32 (Secondary) A slope $p/q$ is characterising for a knot $K \subset \mathbb{S}^3$ if the orientation-preserving homeomorphism type of the manifold $\mathbb{S}^3_K(p/q)$ obtained by performing Dehn surgery of slope $p/q$ along $K$ uniquely determines the knot $K$. We combine new applications of results from hyperbolic geometry with previous individual work of the authors to determine, for any given knot $K$, an explicit bound $\mathcal{C}(K)$ such that $|q| > \mathcal{C}(K)$ implies that $p/q$ is a characterising slope for $K$. Furthermore, we find an optimal such $\mathcal{C}(K)$ for certain satellite knots with winding number zero patterns. |
| title | Effective bounds on characterising slopes for all knots |
| topic | Geometric Topology 57K10 (Primary), 57K30, 57K32 (Secondary) |
| url | https://arxiv.org/abs/2410.24209 |