Barcode entropy and relative symplectic cohomology
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917216937574400 |
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| author | Ahn, Jonghyeon |
| author_facet | Ahn, Jonghyeon |
| contents | In this paper, we study the barcode entropy--the exponential growth rate of the number of not-too-short bars--of the persistence module associated with the relative symplectic cohomology $SH_M(K)$ of a Liouville domain $K$ embedded in a symplectic manifold $M$. Our main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on $\partial K$. More precisely, we show that the barcode entropy of the relative symplectic cohomology $SH_M(K)$ is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of $K$ into $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15606 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Barcode entropy and relative symplectic cohomology Ahn, Jonghyeon Symplectic Geometry In this paper, we study the barcode entropy--the exponential growth rate of the number of not-too-short bars--of the persistence module associated with the relative symplectic cohomology $SH_M(K)$ of a Liouville domain $K$ embedded in a symplectic manifold $M$. Our main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on $\partial K$. More precisely, we show that the barcode entropy of the relative symplectic cohomology $SH_M(K)$ is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of $K$ into $M$. |
| title | Barcode entropy and relative symplectic cohomology |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2601.15606 |