1 results
$C^0$-limits of Legendrians and positive loops
- Part of
-
- Journal:
- Compositio Mathematica / Volume 160 / Issue 12 / December 2024
- Published online by Cambridge University Press:
- 10 March 2025, pp. 2904-2915
- Print publication:
- December 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We show that the image of a properly embedded Legendrian submanifold under a homeomorphism that is the
$C^0$-limit of a sequence of contactomorphisms supported in some fixed compact subset is again Legendrian, if the image of the submanifold is smooth. In proving this, we show that any closed 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 properly embedded non-Legendrians.
