Parametrized homology via zigzag persistence

DOI10.2140/agt.2019.19.657zbMath1427.55005arXiv1604.03596OpenAlexW3101169600MaRDI QIDQ2000778

Dmitriy Morozov, Sara Kališnik Verovšek, Gunnar Carlsson, Vin De Silva

Publication date: 28 June 2019

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03596

zbMATH Keywords

persistent homologylevelset zigzag persistencezigzag persistenceextended persistence

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Homology and cohomology theories in algebraic topology (55N99)

Related Items (5)

Capturing dynamics of time-varying data via topology ⋮ Decomposition of exact pfd persistence bimodules ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ On the structure of double complexes ⋮ Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology

Cites Work

• Categorified Reeb graphs
• Alexander duality for parametrized homology
• Finiteness of rank invariants of multidimensional persistent homology groups
• Extreme elevation on a 2-manifold
• Stability of persistence diagrams
• Extending persistence using Poincaré and Lefschetz duality
• Mapping Hilbert cube manifolds to ANR's: A solution of a conjecture of Borsuk
• Topology of angle valued maps, bar codes and Jordan blocks
• Computing persistent homology
• Topological persistence and simplification
• Homology and robustness of level and interlevel sets
• Zigzag persistence
• Topological persistence for circle-valued maps
• A refinement of Betti numbers and homology in the presence of a continuous function. I
• Stability of critical points with interval persistence
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• Betti numbers in multidimensional persistent homology are stable functions
• The Structure and Stability of Persistence Modules
• Induced Matchings of Barcodes and the Algebraic Stability of Persistence
• Representation Theory of Artin Algebras II
• Decomposition of pointwise finite-dimensional persistence modules
• Proximity of persistence modules and their diagrams
• Zigzag persistent homology and real-valued functions
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
• Algorithms in real algebraic geometry

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