Barcode entropy and wrapped Floer homology

TL;DR

This paper introduces the concept of barcode entropy in wrapped Floer homology, proving it as a contact boundary invariant that provides a lower bound for the Reeb flow's topological entropy, without restrictive assumptions.

Contribution

It establishes barcode entropy as a new invariant of contact boundaries and links it to the dynamical complexity of Reeb flows in Liouville domains.

Findings

Barcode entropy is invariant under different fillings.

It provides a lower bound for Reeb flow topological entropy.

No assumptions on first Chern class or contact form are needed.

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.