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Bibliographic Details
Main Authors: Rizell, Georgios Dimitroglou, Sullivan, Michael G.
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2212.09190
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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