Existence of Reeb Chords from the Generation-Criteria

Abstract

We give some existence results of Reeb chords using the $\textit{generation-criteria}$ of the Fukaya category. In particular, for $n\geq3$, we construct a Legendrian $\ell'\subset S^*\mathbb T^n$ such that every closed spin Legendrian $\ell\subset S^*\mathbb T^n$ either admits a self-Reeb chord or a Reeb chord joining it to $\ell'$.