Barcode entropy and wrapped Floer homology

Abstract

In this paper, we explore the interplay between barcode and topological entropies. Wrapped Floer homology barcode entropy is the exponential growth of not-to-short bars in the persistence module associated with the filtered wrapped Floer homology. We prove that the barcode entropy is an invariant of the contact boundary of a Liouville domain, i.e., does not depend on the filling, and it bounds from below the topological entropy of the Reeb flow. We make no assumptions on the first Chern class of the Liouville domain or the contact form.