Persistent extensions and analogous bars: data-induced relations between persistence barcodes

DOI10.1007/s41468-023-00115-yarXiv2201.05190MaRDI QIDQ6074057

Chad Giusti, Robert W. Ghrist, Hee Rhang Yoon

Publication date: 18 September 2023

Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.05190

zbMATH Keywords

persistence moduleswitness complexhomology class relationspersistent homological algebra

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Computational aspects of data analysis and big data (68T09)

Cites Work

• Construction of universal bundles. I
• Computing persistent homology
• Topological persistence and simplification
• Zigzag persistence
• The persistent homology of a sampled map: from a viewpoint of quiver representations
• A functorial Dowker theorem and persistent homology of asymmetric networks
• Topological spaces of persistence modules and their properties
• Homology groups of relations
• Topology and data
• Induced Matchings of Barcodes and the Algebraic Stability of Persistence
• Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem
• Sparse Circular Coordinates via Principal $$\mathbb {Z}$$-Bundles
• Stability of persistence diagrams
• Barcodes: The persistent topology of data
• The space of barcode bases for persistence modules
• Partial matchings induced by morphisms between persistence modules

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