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arXiv · 2606.09164

A lower bound for relative symplectic cohomology barcode entropy

Jonghyeon Ahn
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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 $\partial K$ 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.

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Jonghyeon Ahn. 2026-06-08. A lower bound for relative symplectic cohomology barcode entropy. https://arxiv.org/abs/2606.09164

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