Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension

DOI10.4230/LIPIcs.SoCG.2018.15zbMath1493.55002arXiv1803.05722MaRDI QIDQ5115782

Emerson G. Escolar, Mickaël Buchet

Publication date: 18 August 2020

Full work available at URL: https://arxiv.org/abs/1803.05722

zbMATH Keywords

quiversrepresentation theorypersistent homologycommutative laddersVietoris-Rips filtrationmulti-persistence

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31)

Related Items (7)

On interval decomposability of \(2\)D persistence modules ⋮ The space of barcode bases for persistence modules ⋮ Partial matchings induced by morphisms between persistence modules ⋮ Approximation by interval-decomposables and interval resolutions of persistence modules ⋮ Every 1D persistence module is a restriction of some indecomposable 2D persistence module ⋮ Computing the interleaving distance is NP-hard ⋮ Computing invariants for multipersistence via spectral systems and effective homology

Uses Software

• CliqueTop

Cites Work

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• The theory of multidimensional persistence
• Matrix method for persistence modules on commutative ladders of finite type
• Topological persistence and simplification
• Zigzag persistence
• Clique topology reveals intrinsic geometric structure in neural correlations
• Introduction to the Representation Theory of Algebras
• Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis
• Stratifying Multiparameter Persistent Homology
• Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology
• Persistence modules on commutative ladders of finite type

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