Algebraic stability of zigzag persistence modules
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Publication:1631693
DOI10.2140/agt.2018.18.3133zbMath1432.55011arXiv1604.00655OpenAlexW2335810221MaRDI QIDQ1631693
Magnus Bakke Botnan, Michael Lesnick
Publication date: 6 December 2018
Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.00655
Persistent homology and applications, topological data analysis (55N31) Applied homological algebra and category theory in algebraic topology (55U99)
Related Items (28)
On interval decomposability of \(2\)D persistence modules ⋮ Universality of persistence diagrams and the bottleneck and Wasserstein distances ⋮ Universality of the homotopy interleaving distance ⋮ Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications ⋮ Local characterizations for decomposability of 2-parameter persistence modules ⋮ Persistence and the Sheaf-Function Correspondence ⋮ On the Stability of Multigraded Betti Numbers and Hilbert Functions ⋮ Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem ⋮ Analysis of Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence ⋮ Decomposition of persistence modules ⋮ Computing the interleaving distance is NP-hard ⋮ Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 ⋮ Spatiotemporal persistent homology for dynamic metric spaces ⋮ Computational Complexity of the Interleaving Distance ⋮ On the stability of interval decomposable persistence modules ⋮ Elder-Rule-Staircodes for Augmented Metric Spaces ⋮ Decomposition of exact pfd persistence bimodules ⋮ Towards the prediction of critical transitions in spatially extended populations with cubical homology ⋮ Unnamed Item ⋮ On the geometrical properties of the coherent matching distance in 2D persistent homology ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Topological spaces of persistence modules and their properties ⋮ The reflection distance between zigzag persistence modules ⋮ Generalized persistence algorithm for decomposing multiparameter persistence modules ⋮ Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology ⋮ On rectangle-decomposable 2-parameter persistence modules ⋮ Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology ⋮ Interval decomposition of infinite zigzag persistence modules
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