A derived isometry theorem for sheaves

DOI10.1016/j.aim.2021.108033zbMath1487.55007arXiv1805.09694OpenAlexW3202466162MaRDI QIDQ2064473

Nicolas Berkouk, Grégory Ginot

Publication date: 6 January 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.09694

zbMATH Keywords

sheavestopological data analysispersistent homologybarcodesisometry theoremconvolution distance

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Derived categories, triangulated categories (18G80)

Related Items (3)

Piecewise Linear Sheaves ⋮ Thickening of the diagonal and interleaving distance ⋮ Persistence and the Sheaf-Function Correspondence

Cites Work

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• The observable structure of persistence modules
• Stability of persistence diagrams
• The theory of multidimensional persistence
• Injective choice functions for countable families
• Quillen closed model structures for sheaves
• Persistence-like distance on Tamarkin's category and symplectic displacement energy
• Decomposition of exact pfd persistence bimodules
• Persistent homology and microlocal sheaf theory
• The theory of the interleaving distance on multidimensional persistence modules
• Ephemeral persistence modules and distance comparison
• The Structure and Stability of Persistence Modules
• Decomposition of pointwise finite-dimensional persistence modules
• Interval decomposition of infinite zigzag persistence modules
• Proximity of persistence modules and their diagrams

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