Characterizing slopes for satellite knots
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911935309545472 |
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| author | Sorya, Patricia |
| author_facet | Sorya, Patricia |
| contents | A slope $p/q$ is said to be characterizing for a knot $K$ if the homeomorphism type of the $p/q$-Dehn surgery along $K$ determines the knot up to isotopy. Extending previous work of Lackenby and McCoy on hyperbolic and torus knots respectively, we study satellite knots to show that for a knot $K$, any slope $p/q$ is characterizing provided $|q|$ is sufficiently large. In particular, we establish that every non-integral slope is characterizing for a composite knot. Our approach consists of a detailed examination of the JSJ decomposition of a surgery along a knot, combined with results from other authors giving constraints on surgery slopes that yield manifolds containing certain surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00739 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizing slopes for satellite knots Sorya, Patricia Geometric Topology A slope $p/q$ is said to be characterizing for a knot $K$ if the homeomorphism type of the $p/q$-Dehn surgery along $K$ determines the knot up to isotopy. Extending previous work of Lackenby and McCoy on hyperbolic and torus knots respectively, we study satellite knots to show that for a knot $K$, any slope $p/q$ is characterizing provided $|q|$ is sufficiently large. In particular, we establish that every non-integral slope is characterizing for a composite knot. Our approach consists of a detailed examination of the JSJ decomposition of a surgery along a knot, combined with results from other authors giving constraints on surgery slopes that yield manifolds containing certain surfaces. |
| title | Characterizing slopes for satellite knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2307.00739 |