On Categorical Entropy from the viewpoint of Symplectic Topology
Hanwool Bae, Dongwook Choa, Wonbo Jeong, Dogancan Karabas, Sangjin Lee

TL;DR
This paper investigates categorical entropy within symplectic topology, establishing relations with localization, providing computational methods for Fukaya categories, and exploring duality properties that enable entropy calculation from morphism spaces.
Contribution
It introduces new relations between categorical entropy and localization, offers a method to compute entropy in Fukaya categories, and demonstrates entropy calculation via duality in symplectic manifolds.
Findings
Relation between categorical entropy and localization established
Method for calculating categorical entropy in Fukaya categories provided
Existence of duality in Fukaya categories enabling entropy computation from morphisms
Abstract
In this paper, motivated by symplectic topology, we explore categorical entropy and present two main results. The first result establishes a relation between categorical entropies of functors on a category and its localization. Additionally, it demonstrates analogies between the notions of topological and categorical entropy. This result is then applied to symplectic topology, where we provide a method for calculating the categorical entropy of a functor on a (partially) wrapped Fukaya category, assuming that the functor is induced by a compactly supported symplectic automorphism. For the second main result of the paper, we observe the existence of natural examples of symplectic manifolds whose Fukaya categories satisfy a type of Floer-theoretic duality. Motivated by this observation, we prove that categorical entropy can be computed from the morphism spaces under the assumption of…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Topological and Geometric Data Analysis
