Homological algebra for persistence modules

DOI10.1007/s10208-020-09482-9zbMath1487.55008arXiv1905.05744OpenAlexW3118771332MaRDI QIDQ2052717

Nikola Milićević, Peter Bubenik

Publication date: 26 November 2021

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05744

zbMATH Keywords

Grothendieck categoriesgraded modulessheavespersistent homologyhomological algebraKünneth theoremsuniversal coefficient theorems

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Projectives and injectives (category-theoretic aspects) (18G05) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Homology of a product, Künneth formula (55U25)

Related Items (5)

Field choice problem in persistent homology ⋮ Exact weights, path metrics, and algebraic Wasserstein distances ⋮ Homological approximations in persistence theory ⋮ Persistent homology of the sum metric ⋮ The persistent homology of dual digital image constructions

Cites Work

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• Metrics for generalized persistence modules
• The theory of multidimensional persistence
• A note on the structure of injective diagrams
• Sheaves in topology
• Computing persistent homology
• On monoid graded local rings.
• Persistent magnitude
• Categorification of persistent homology
• Persistent homology of the sum metric
• Persistent homology and microlocal sheaf theory
• Topological spaces of persistence modules and their properties
• The theory of the interleaving distance on multidimensional persistence modules
• Endlich präsentierbare Moduln
• Sur quelques points d'algèbre homologique
• Modules \(M\) such that \(\mathrm{Ext}_R^1(M,-)\) commutes with direct limits.
• Ephemeral persistence modules and distance comparison
• Graded Rings and Graded Grothendieck Groups
• Decompositions of Monomial Ideals in Real Semigroup Rings
• Decomposition of persistence modules
• Stratifying Multiparameter Persistent Homology
• Persistence modules with operators in Morse and Floer theory

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