A lower bound for relative symplectic cohomology barcode entropy

2026/06/08 by Jonghyeon Ahn · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

In this paper, we continue to study the barcode entropy of relative symplectic cohomology SH_M(K) of a Liouville domain K embedded in a symplectic manifold M. This barcode entropy measures the exponential growth rate of the number of not-too-short bars in the persistence module SH_M(K). We prove that this Floer-theoretic invariant admits a nontrivial lower bound in terms of the topological entropy of the Reeb flow on ∂ K when the Reeb flow possesses a hyperbolic invariant set. More precisely, we show that the barcode entropy of SH_M(K) is bounded below by the topological entropy of the Reeb flow restricted to a hyperbolic invariant set.

Citations

• Barcode entropy and relative symplectic cohomology
• Comparison of symplectic capacities
• Wrapped Floer homology and hyperbolic sets
• Barcode entropy and wrapped Floer homology
• S¹-equivariant relative symplectic cohomology and relative symplectic capacities
• On the barcode entropy of Lagrangian submanifolds
• On the Barcode Entropy of Reeb Flows
• Invariant Sets and Hyperbolic Closed Reeb Orbits
• Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective
• Symplectic topology and ideal-valued measures
• Autonomous Hamiltonian flows, Hofer's geometry and persistence modules
• The structure and stability of persistence modules

Discussions

• Jonghyeon Ahn: A lower bound for relative symplectic cohomology barcode entropy https://arxiv.org/abs/2606.09164 https://arxiv.org/pdf/2606.09164 https://arxiv.org/html/2606.09164 [bsky, 0 points, 0 comments]

Related

• Barcode entropy and relative symplectic cohomology
• On the Barcode Entropy of Reeb Flows
• Topics in Symplectic Dynamics: Barcode Entropy
• On the barcode entropy of Lagrangian submanifolds
• Persistent Entropy of Floer Persistence Barcodes