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A property of the interleaving distance for sheaves: research article

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\-modul...

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Bibliographic Details
Main Authors: Petit, François (Author) , Schapira, Pierre (Author) , Waas, Lukas (Author)
Format: Article (Journal)
Language:English
Published: January 2025
In: Bulletin of the London Mathematical Society
Year: 2025, Volume: 57, Issue: 1, Pages: 137-149
ISSN:1469-2120
DOI:10.1112/blms.13187
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1112/blms.13187
Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1112/blms.13187
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Author Notes:François Petit, Pierre Schapira, Lukas Waas
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Summary: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.
Item Description:Online verfügbar: 17. November 2024
Gesehen am 21.05.2025
Physical Description:Online Resource
ISSN:1469-2120
DOI:10.1112/blms.13187

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