Constructions and Isotopies of High-Dimensional Legendrian Spheres
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915356348514304 |
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| author | Roy, Agniva |
| author_facet | Roy, Agniva |
| contents | We explore the construction of Legendrian spheres in contact manifolds of any dimension. Two constructions involving open books work in any contact manifold, while one introduced by Ekholm works only in $\mathbb{R}^{2n+1}$. We show that these three constructions are isotopic to the Legendrian unknot, thus recovering and generalising a result of Courte and Ekholm, that shows Ekholm's doubling procedure produces the standard Legendrian unknot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00773 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Constructions and Isotopies of High-Dimensional Legendrian Spheres Roy, Agniva Symplectic Geometry Geometric Topology 57R17 We explore the construction of Legendrian spheres in contact manifolds of any dimension. Two constructions involving open books work in any contact manifold, while one introduced by Ekholm works only in $\mathbb{R}^{2n+1}$. We show that these three constructions are isotopic to the Legendrian unknot, thus recovering and generalising a result of Courte and Ekholm, that shows Ekholm's doubling procedure produces the standard Legendrian unknot. |
| title | Constructions and Isotopies of High-Dimensional Legendrian Spheres |
| topic | Symplectic Geometry Geometric Topology 57R17 |
| url | https://arxiv.org/abs/2211.00773 |