Non-Simple knots in Contact 3-Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918263970070528 |
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| author | Datta, Ipsita Shah, Tanushree |
| author_facet | Datta, Ipsita Shah, Tanushree |
| contents | We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are topologically isotopic to the $n$-twist knot in a Lens space $L(α, β)$ than in $S^3$. We also include connect sum formulas for rational variants of classical invariants, $\mathrm{tb}_\mathbb{Q}$, $\mathrm{rot}_\mathbb{Q}$, and $\mathrm{sl}_\mathbb{Q}$, which indicate that prime knots are the right playground to look for exotic behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Simple knots in Contact 3-Manifolds Datta, Ipsita Shah, Tanushree Geometric Topology Symplectic Geometry 57K33, 53D10 We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are topologically isotopic to the $n$-twist knot in a Lens space $L(α, β)$ than in $S^3$. We also include connect sum formulas for rational variants of classical invariants, $\mathrm{tb}_\mathbb{Q}$, $\mathrm{rot}_\mathbb{Q}$, and $\mathrm{sl}_\mathbb{Q}$, which indicate that prime knots are the right playground to look for exotic behaviour. |
| title | Non-Simple knots in Contact 3-Manifolds |
| topic | Geometric Topology Symplectic Geometry 57K33, 53D10 |
| url | https://arxiv.org/abs/2510.02932 |