Connectedness and Lusternik-Schnirelmann categories of the spaces of persistence modules

zbMath1505.55014MaRDI QIDQ2190812

Tane Vergili

Publication date: 22 June 2020

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://nyjm.albany.edu/j/2020/26-27.html

zbMATH Keywords

persistent homologyinterleaving distancepersistence modules

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Functor categories, comma categories (18A25) Applications of general topology to computer science (e.g., digital topology, image processing) (54H30)

Cites Work

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• The observable structure of persistence modules
• Stability of persistence diagrams
• Metrics for generalized persistence modules
• Categorification of persistent homology
• Topological spaces of persistence modules and their properties
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• The Structure and Stability of Persistence Modules
• Decomposition of pointwise finite-dimensional persistence modules
• Higher Interpolation and Extension for Persistence Modules
• Proximity of persistence modules and their diagrams

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