Decomposition of persistence modules

DOI10.1090/proc/14790zbMath1461.16013arXiv1811.08946OpenAlexW2982539600MaRDI QIDQ5119216

William Crawley-Boevey, Magnus Bakke Botnan

Publication date: 3 September 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08946

zbMATH Keywords

persistence moduletopological data analysis

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Representations of quivers and partially ordered sets (16G20)

Related Items (20)

Computing persistent Stiefel-Whitney classes of line bundles ⋮ Persistence landscapes of affine fractals ⋮ Ephemeral persistence modules and distance comparison ⋮ Composition series of arbitrary cardinality in modular lattices and abelian categories ⋮ Universality of the homotopy interleaving distance ⋮ Decomposition of pointwise finite-dimensional 𝕊1 persistence modules ⋮ Continuous quivers of type \(A\) (IV). Continuous mutation and geometric models of \textbf{E}-clusters ⋮ Local characterizations for decomposability of 2-parameter persistence modules ⋮ Approximation by interval-decomposables and interval resolutions of persistence modules ⋮ Exact weights, path metrics, and algebraic Wasserstein distances ⋮ Recovering the homology of immersed manifolds ⋮ Homological approximations in persistence theory ⋮ Persistent magnitude ⋮ On the stability of interval decomposable persistence modules ⋮ Decomposition of exact pfd persistence bimodules ⋮ Homological algebra for persistence modules ⋮ Decorated merge trees for persistent topology ⋮ On rectangle-decomposable 2-parameter persistence modules ⋮ CONTINUOUS QUIVERS OF TYPE A (III) EMBEDDINGS OF CLUSTER THEORIES ⋮ Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology

Cites Work

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• Representation theory of Dynkin quivers. Three contributions
• The theory of multidimensional persistence
• A note on the structure of injective diagrams
• Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
• Algebraic stability of zigzag persistence modules
• Decomposition of exact pfd persistence bimodules
• Topology and data
• Locally finitely presented additive categories
• Decomposition of pointwise finite-dimensional persistence modules
• Interval decomposition of infinite zigzag persistence modules
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem

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