Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology

DOI10.1007/s13160-022-00517-yOpenAlexW3172478926MaRDI QIDQ2111545

Haibin Hang, Washington Mio

Publication date: 17 January 2023

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.08557

zbMATH Keywords

persistent homologypersistence diagramscorrespondence modulespersistence sheaves

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Topological data analysis (62R40)

Cites Work

• Stability of persistence diagrams
• The theory of multidimensional persistence
• Extending persistence using Poincaré and Lefschetz duality
• Generalized persistence diagrams
• Algebraic stability of zigzag persistence modules
• Numeric invariants from multidimensional persistence
• Computing persistent homology
• Topological persistence and simplification
• Zigzag persistence
• Parametrized homology via zigzag persistence
• Decomposition of exact pfd persistence bimodules
• A topological study of functional data and Fréchet functions of metric measure spaces
• Persistent homology and microlocal sheaf theory
• The persistent homotopy type distance
• The theory of the interleaving distance on multidimensional persistence modules
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• The Structure and Stability of Persistence Modules
• A distance for similarity classes of submanifolds of a Euclidean space
• Decomposition of pointwise finite-dimensional persistence modules
• Decomposition of persistence modules
• Proximity of persistence modules and their diagrams
• Zigzag persistent homology and real-valued functions
• PERSISTENCE BARCODES FOR SHAPES
• Statistical topological data analysis using persistence landscapes
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