Existence of Reeb Chords from the Generation-Criteria

Abstract

We give some existence results of Reeb chords using the $\text{generation-criteria}$ of the Fukaya category. In particular, for $n\ge 3$, we construct a Legendrian ${\ell }^{\prime }\subset S^{\ast }{\mathbb{T}}^n$ such that every closed spin Legendrian $\ell \subset S^{\ast }{\mathbb{T}}^n$ either admits a self-Reeb chord or a Reeb chord joining it to ${\ell }^{\prime }$.