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A COMPARISON OF CATEGORICAL AND TOPOLOGICAL ENTROPIES ON WEINSTEIN MANIFOLDS

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  17 February 2025

HANWOOL BAE Open the ORCID record for HANWOOL BAE [Opens in a new window]  and
SANGJIN LEE Open the ORCID record for SANGJIN LEE [Opens in a new window]
HANWOOL BAE
Affiliation:
Center for Quantum Structures in Modules and Spaces Seoul National University Seoul, South Korea hanwoolb@gmail.com
SANGJIN LEE*
Affiliation:
Center for Geometry and Physics Institute for Basic Science (IBS) Pohang 37673, Korea sangjinlee@ibs.re.kr
*
sangjinlee@kias.re.kr
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Abstract

Let W be a symplectic manifold, and let $\phi :W \to W$ be a symplectic automorphism. This automorphism induces an auto-equivalence $\Phi $ defined on the Fukaya category of W. In this paper, we prove that the categorical entropy of $\Phi $ provides a lower bound for the topological entropy of $\phi $, where W is a Weinstein manifold and $\phi $ is compactly supported. Furthermore, motivated by [cCGG24], we propose a conjecture that generalizes the result of [New88, Prz80, Yom87].

Keywords

categorical entropytopological entropysymplectic automorphism

MSC classification

Primary: 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
Secondary: 53D40: Floer homology and cohomology, symplectic aspects

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Article
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Nagoya Mathematical Journal , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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