A property of the interleaving distance for sheaves

• Verfasst von: Petit, François [VerfasserIn]
• Verfasst von: Schapira, Pierre [VerfasserIn]
• Verfasst von: Waas, Lukas [VerfasserIn]
• Titel: A property of the interleaving distance for sheaves
• Titelzusatz: research article
• Verf.angabe: François Petit, Pierre Schapira, Lukas Waas
• E-Jahr: 2025
• Jahr: January 2025
• Umfang: 13 S.
• Fussnoten: Online verfügbar: 17. November 2024 ; Gesehen am 21.05.2025
• Titel Quelle: Enthalten in: London Mathematical SocietyBulletin of the London Mathematical Society
• Ort Quelle: Hoboken, NJ : Wiley, 1969
• Jahr Quelle: 2025
• Band/Heft Quelle: 57(2025), 1, Seite 137-149
• ISSN Quelle: 1469-2120
• DOI: doi:10.1112/blms.13187
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1926233077

Abstract

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.