A comparison of categorical and topological entropies on Weinstein manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911184201973760 |
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| author | Bae, Hanwool Lee, Sangjin |
| author_facet | Bae, Hanwool Lee, Sangjin |
| contents | Let $W$ be a symplectic manifold, and let $ϕ:W \to W$ be a symplectic automorphism. Then, $ϕ$ induces an auto-equivalence $Φ$ defined on the Fukaya category of $W$. In this paper, we prove that the categorical entropy of $Φ$ bounds the topological entropy of $ϕ$ from below where $W$ is a Weinstein manifold and $ϕ$ is compactly supported. Moreover, being motivated by the work of Cineli, Ginzburg, and Gurel, we propose a conjecture which generalizes a result in dynamical system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14597 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A comparison of categorical and topological entropies on Weinstein manifolds Bae, Hanwool Lee, Sangjin Symplectic Geometry 53D37, 53D40, 37J11 Let $W$ be a symplectic manifold, and let $ϕ:W \to W$ be a symplectic automorphism. Then, $ϕ$ induces an auto-equivalence $Φ$ defined on the Fukaya category of $W$. In this paper, we prove that the categorical entropy of $Φ$ bounds the topological entropy of $ϕ$ from below where $W$ is a Weinstein manifold and $ϕ$ is compactly supported. Moreover, being motivated by the work of Cineli, Ginzburg, and Gurel, we propose a conjecture which generalizes a result in dynamical system. |
| title | A comparison of categorical and topological entropies on Weinstein manifolds |
| topic | Symplectic Geometry 53D37, 53D40, 37J11 |
| url | https://arxiv.org/abs/2208.14597 |