$C^0$-limits of Legendrians and positive loops
Symplectic Geometry
2025-03-19 v4
Abstract
We show that the image of a Legendrian submanifold under a homeomorphism that is the -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.
Keywords
Cite
@article{arxiv.2212.09190,
title = {$C^0$-limits of Legendrians and positive loops},
author = {Georgios Dimitroglou Rizell and Michael G. Sullivan},
journal= {arXiv preprint arXiv:2212.09190},
year = {2025}
}
Comments
V2: Added two references and Remark 2.7. V3: Removed one lemma in Section 3.2, resulting in slightly adjusted subsequent lemmas from that section. V4: Weakened Theorem C to closed Legendrians