1. $C^0$-limits of Legendrians and positive loops
- Author
-
Rizell, Georgios Dimitroglou and Sullivan, Michael G.
- Subjects
Mathematics - Symplectic Geometry ,53D10 - Abstract
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., Comment: 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
- Published
- 2022