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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 $\phi:W \to W$ be a symplectic automorphism. Then, $\phi$ induces an auto-equivalence $\Phi$ defined on the Fukaya category of $W$. In this paper, we prove that the categorical entropy of $\Phi$ bounds the topological entropy of $\phi$ from below where $W$ is a Weinstein manifold and $\phi$ 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. 2022-08-31. A comparison of categorical and topological entropies on Weinstein manifolds. https://doi.org/10.1017/nmj.2025.3

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