2020/06/12 by Yasuaki Hiraoka, Hiraoka, Yasuaki, Yuichi Ike +3 · 1 citation
Computer Science · Mathematics · #16E35 #16G20 #35A27 #55N99 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2006.06924
openalex publication_date 2020/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.