Critical edges in Rips complexes and persistence

DOI10.1007/s00009-023-02533-9arXiv2304.05185OpenAlexW4388293925MaRDI QIDQ6141238

Žiga Virk, Peter Goričan

Publication date: 22 January 2024

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.05185

zbMATH Keywords

persistent homologycritical simplexrips complexreconstruction result

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31)

Cites Work

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• On the definition of the homological critical value
• Persistence stability for geometric complexes
• Thick Spanier groups and the first shape group
• The observable structure of persistence modules
• Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability
• Topological persistence and simplification
• Contractions in persistence and metric graphs
• A counter-example to Hausmann's conjecture
• Footprints of geodesics in persistent homology
• Categorification of persistent homology
• The Vietoris-Rips complexes of a circle
• On the fundamental groups of one-dimensional spaces
• Rips complexes as nerves and a functorial Dowker-nerve diagram
• The Morse theory of Čech and Delaunay complexes
• An alternate proof that the fundamental group of a Peano continuum is finitely presented if the group is countable
• Reconstruction properties of selective Rips complexes
• 1-Dimensional intrinsic persistence of geodesic spaces
• On Vietoris–Rips complexes of ellipses

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