论文标题
Hochschild熵和分类熵
Hochschild entropy and Categorical entropy
论文作者
论文摘要
我们通过Sheridan-Smith建立的K3表面的同源镜子对称性，研究了分类熵和反示例。我们介绍了DG类别的准内膜渐近不变的，称为Hochschild熵。事实证明，分类熵是由霍基柴尔德熵限制的。此外，在Thurston的经典结果的驱动下，我们证明了存在的正性托雷利映射类别的积极分类熵。我们还考虑与浮动理论熵的关系。
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.
