Persistence Homology in Symplectic and Contact Topology

On the strong Arnold chord conjecture for convex contact forms

15 juin 2023, 14:30

1h

Albi

Orateur

Jungsoo Kang

Description

Arnold conjectured that every closed Legendrian submanifold in the standard contact sphere $S^{2n-1}$ with a contact form has a Reeb chord. This was confirmed by K. Mohnke in 2001. In fact, Arnold originally conjectured that a Reeb chord with distinct endpoints exists. I will give a proof of this strong version of the conjecture for convex contact forms, namely contact forms on $S^{2n-1}$ induced by convex embeddings into ${\mathbb{R}}^{2n}$. I will also present a counterexample to the conjecture for nonconvex contact forms due to M. Hutchings.