Čech-Delaunay gradient flow and homology inference for self-maps

DOI10.1007/s41468-020-00058-8zbMath1479.55010arXiv1709.04068OpenAlexW3082060182MaRDI QIDQ2221301

Marian Mrozek, Ulrich Bauer, Grzegorz Jabłoński, Herbert Edelsbrunner

Publication date: 26 January 2021

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

Full work available at URL: https://arxiv.org/abs/1709.04068

zbMATH Keywords

persistent homologycomputational topology

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Topological dynamics (37B99) Simplicial sets and complexes in algebraic topology (55U10) Numerical problems in dynamical systems (65P99) Topological data analysis (62R40) Discrete Morse theory and related ideas in manifold topology (57Q70)

Related Items (5)

Persistence of Morse decompositions over grid resolution for maps and time series ⋮ Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems ⋮ A unified view on the functorial nerve theorem and its variations ⋮ Configuration spaces of disks in an infinite strip ⋮ Conley Index Approach to Sampled Dynamics

Uses Software

• Miniball

Cites Work

• The persistent homology of a self-map
• Morse theory for cell complexes
• Computational homology
• Computing persistent homology
• Topological persistence and simplification
• Reconstructing functions from random samples
• The Morse theory of Čech and Delaunay complexes
• Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
• Towards persistence-based reconstruction in euclidean spaces
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