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arXiv · 2208.14597

A comparison of categorical and topological entropies on Weinstein manifolds

Hanwool Bae·Sangjin Lee
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Abstract

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.

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Hanwool Bae, Sangjin Lee. 2025-02-03. A comparison of categorical and topological entropies on Weinstein manifolds. https://doi.org/10.1017/nmj.2025.3

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