Knots that share four surgeries
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913874232475648 |
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| author | Kegel, Marc Piccirillo, Lisa |
| author_facet | Kegel, Marc Piccirillo, Lisa |
| contents | Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct knots K,K' that have common Dehn surgeries for four distinct slopes. We also construct non-isotopic Legendrian knots K,K' that have contactomorphic contact (+1)-and (-1)-surgeries, disproving an analogous conjecture in contact geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knots that share four surgeries Kegel, Marc Piccirillo, Lisa Geometric Topology Symplectic Geometry 57R65, 57K10, 57R65, 57R58, 57K16, 57K14, 57K32 Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct knots K,K' that have common Dehn surgeries for four distinct slopes. We also construct non-isotopic Legendrian knots K,K' that have contactomorphic contact (+1)-and (-1)-surgeries, disproving an analogous conjecture in contact geometry. |
| title | Knots that share four surgeries |
| topic | Geometric Topology Symplectic Geometry 57R65, 57K10, 57R65, 57R58, 57K16, 57K14, 57K32 |
| url | https://arxiv.org/abs/2505.13168 |