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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.09190 |
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| _version_ | 1866913742994800640 |
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| author | Rizell, Georgios Dimitroglou Sullivan, Michael G. |
| author_facet | Rizell, Georgios Dimitroglou Sullivan, Michael G. |
| contents | We show that the image of a Legendrian submanifold under a homeomorphism that is the $C^0$-limit of a sequence of contactomorphisms is again Legendrian, if the image of the submanifold is smooth. In proving this, we show that any non-Legendrian submanifold of a contact manifold admits a positive loop and we provide a parametric refinement of the Rosen--Zhang result on the degeneracy of the Chekanov--Hofer--Shelukhin pseudo-norm for non-Legendrians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09190 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $C^0$-limits of Legendrians and positive loops Rizell, Georgios Dimitroglou Sullivan, Michael G. Symplectic Geometry 53D10 We show that the image of a Legendrian submanifold under a homeomorphism that is the $C^0$-limit of a sequence of contactomorphisms is again Legendrian, if the image of the submanifold is smooth. In proving this, we show that any non-Legendrian submanifold of a contact manifold admits a positive loop and we provide a parametric refinement of the Rosen--Zhang result on the degeneracy of the Chekanov--Hofer--Shelukhin pseudo-norm for non-Legendrians. |
| title | $C^0$-limits of Legendrians and positive loops |
| topic | Symplectic Geometry 53D10 |
| url | https://arxiv.org/abs/2212.09190 |