Algebraic stability theorem for derived categories of zigzag persistence modules
Algebraic stability theorem for derived categories of zigzag persistence modules
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Zigzag 持久性模块派生类别的代数稳定性定理
DOI：
10.1142/s1793525322500091
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发表时间：
2022
影响因子：
0.8
通讯作者：
Yoshiwaki Michio
中科院分区：
文献类型：
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作者：
Hiraoka Yasuaki;Ike Yuichi;Yoshiwaki Michio
从派生范畴和Auslander-Reiten抖动的角度研究了锯齿形持久模的距离。普通持久化模块的派生类别等价于任意之字形持久化模块的派生类别，这取决于经典的倾斜模块。通过这个导出的等价，我们定义并计算了任意之字形持久模的导出范畴上的距离，并证明了一个代数稳定性定理。我们还将我们的距离与Botnan-Lesnick引入的纯之形持久模块的距离以及由Kashiwara-Schapira引起的束理论卷积距离进行了比较。
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander–Reiten quivers. The derived category of ordinary persistence modules is derived equivalent to that of arbitrary zigzag persistence modules, depending on a classical tilting module. Through this derived equivalence, we define and compute distances on the derived category of arbitrary zigzag persistence modules and prove an algebraic stability theorem. We also compare our distance with the distance for purely zigzag persistence modules introduced by Botnan–Lesnick and the sheaf-theoretic convolution distance due to Kashiwara–Schapira.