Tight contact structures on some families of small Seifert fiber spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914747306213376 |
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| author | Wan, Shunyu |
| author_facet | Wan, Shunyu |
| contents | Suppose $K$ is a knot in a 3-manifold $Y$, and that $Y$ admits a pair of distinct contact structures. Assume that $K$ has Legendrian representatives in each of these contact structures, such that the corresponding Thurston-Bennequin framings are equivalent. This paper provides a method to prove that the contact structures resulting from Legendrian surgery along these two representatives remain distinct. Applying this method to the situation where the starting manifold is $-Σ(2,3,6m+1)$ and the knot is a singular fiber, together with convex surface theory we can classify the tight contact structures on certain families of Seifert fiber spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10171 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tight contact structures on some families of small Seifert fiber spaces Wan, Shunyu Geometric Topology Suppose $K$ is a knot in a 3-manifold $Y$, and that $Y$ admits a pair of distinct contact structures. Assume that $K$ has Legendrian representatives in each of these contact structures, such that the corresponding Thurston-Bennequin framings are equivalent. This paper provides a method to prove that the contact structures resulting from Legendrian surgery along these two representatives remain distinct. Applying this method to the situation where the starting manifold is $-Σ(2,3,6m+1)$ and the knot is a singular fiber, together with convex surface theory we can classify the tight contact structures on certain families of Seifert fiber spaces. |
| title | Tight contact structures on some families of small Seifert fiber spaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2311.10171 |