Small energy isotopies of loose Legendrian submanifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909444737073152 |
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| author | Nakamura, Lukas |
| author_facet | Nakamura, Lukas |
| contents | We prove that for a closed Legendrian submanifold $L$ of dimension $n \geq 2$ with a loose chart of size $η$, any Legendrian isotopy starting at $L$ can be $C^0$-approximated by a Legendrian isotopy with energy arbitrarily close to $\fracη{2}$. This in particular implies that the displacement energy of loose displaceable Legendrians is bounded by half the size of its smallest loose chart, which proves a conjecture of Dimitroglou Rizell and Sullivan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05970 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Small energy isotopies of loose Legendrian submanifolds Nakamura, Lukas Symplectic Geometry 53D99 We prove that for a closed Legendrian submanifold $L$ of dimension $n \geq 2$ with a loose chart of size $η$, any Legendrian isotopy starting at $L$ can be $C^0$-approximated by a Legendrian isotopy with energy arbitrarily close to $\fracη{2}$. This in particular implies that the displacement energy of loose displaceable Legendrians is bounded by half the size of its smallest loose chart, which proves a conjecture of Dimitroglou Rizell and Sullivan. |
| title | Small energy isotopies of loose Legendrian submanifolds |
| topic | Symplectic Geometry 53D99 |
| url | https://arxiv.org/abs/2105.05970 |