Hochschild Entropy and Categorical Entropy

Q3 Mathematics Arnold Mathematical Journal Pub Date : 2022-07-18 DOI:10.1007/s40598-022-00210-5

Kohei Kikuta, Genki Ouchi

引用次数: 4

Abstract

We study the categorical entropy and counterexamples to Gromov–Yomdin type conjecture via homological mirror symmetry of K3 surfaces established by Sheridan–Smith. We introduce asymptotic invariants of quasi-endofunctors of dg categories, called the Hochschild entropy. It is proved that the categorical entropy is lower bounded by the Hochschild entropy. Furthermore, motivated by Thurston’s classical result, we prove the existence of a symplectic Torelli mapping class of positive categorical entropy. We also consider relations to the Floer-theoretic entropy.

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霍克希尔德熵与范畴熵

通过Sheridan–Smith建立的K3曲面的同源镜像对称性，研究了Gromov–Yomdin型猜想的范畴熵和反例。我们引入了dg范畴的拟内函子的渐近不变量，称为Hochschild熵。证明了范畴熵是霍克希尔德熵的下界。此外，在Thurston经典结果的推动下，我们证明了正分类熵的辛Torelli映射类的存在性。我们还考虑了与Floer理论熵的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Arnold Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.50

自引率

0.00%

发文量

期刊介绍： The Arnold Mathematical Journal publishes interesting and understandable results in all areas of mathematics. The name of the journal is not only a dedication to the memory of Vladimir Arnold (1937 – 2010), one of the most influential mathematicians of the 20th century, but also a declaration that the journal should serve to maintain and promote the scientific style characteristic for Arnold''s best mathematical works. Features of AMJ publications include: Popularity. The journal articles should be accessible to a very wide community of mathematicians. Not only formal definitions necessary for the understanding must be provided but also informal motivations even if the latter are well-known to the experts in the field. Interdisciplinary and multidisciplinary mathematics. AMJ publishes research expositions that connect different mathematical subjects. Connections that are useful in both ways are of particular importance. Multidisciplinary research (even if the disciplines all belong to pure mathematics) is generally hard to evaluate, for this reason, this kind of research is often under-represented in specialized mathematical journals. AMJ will try to compensate for this.Problems, objectives, work in progress. Most scholarly publications present results of a research project in their “final'' form, in which all posed questions are answered. Some open questions and conjectures may be even mentioned, but the very process of mathematical discovery remains hidden. Following Arnold, publications in AMJ will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions. AMJ publishes well-motivated research problems on a regular basis. Problems do not need to be original; an old problem with a new and exciting motivation is worth re-stating. Following Arnold''s principle, a general formulation is less desirable than the simplest partial case that is still unknown.Being interesting. The most important requirement is that the article be interesting. It does not have to be limited by original research contributions of the author; however, the author''s responsibility is to carefully acknowledge the authorship of all results. Neither does the article need to consist entirely of formal and rigorous arguments. It can contain parts, in which an informal author''s understanding of the overall picture is presented; however, these parts must be clearly indicated.

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