A property of the interleaving distance for sheaves: research article - Petit, François; Schapira, Pierre; Waas, Lukas (Bulletin of the London Mathematical Society, 2025)
Let \X\ be a real analytic manifold endowed with a distance satisfying suitable properties and let {\bf k\ be a field. In [Petit and Schapira, Selecta Math. 29 (2023), no. 70, DOI 10.1007/s00029-023-00875-6], the authors construct a pseudo-distance on the derived category of sheaves of {\bf k\-modules on \X\, generalizing a previous construction of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83-113]. We prove here that if the distance between two constructible sheaves with compact support (or more generally, constructible sheaves up to infinity) on \X\ is zero, then these two sheaves are isomorphic, answering a question of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83-113]. We also prove that our results imply a similar statement for finitely presentable persistence modules due to Lesnick.
Online verfügbar: 17. November 2024
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