Contractions in persistence and metric graphs

DOI10.1007/s40840-022-01368-zOpenAlexW4289855226MaRDI QIDQ2082364

Žiga Virk

Publication date: 4 October 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.11478

zbMATH Keywords

Lipschitz mappersistence modulemetric graphpersistent homologypersistence diagramrips complex

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Abstract complexes in algebraic topology (55U05) Lipschitz and coarse geometry of metric spaces (51F30)

Related Items (3)

Rigidity of terminal simplices in persistent homology ⋮ Critical edges in Rips complexes and persistence ⋮ Lower bounds on the homology of Vietoris-Rips complexes of hypercube graphs

Cites Work

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• Persistence stability for geometric complexes
• The observable structure of persistence modules
• Persistent cohomology and circular coordinates
• Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability
• A counter-example to Hausmann's conjecture
• Footprints of geodesics in persistent homology
• The Vietoris-Rips complexes of a circle
• Rips complexes as nerves and a functorial Dowker-nerve diagram
• Induced Matchings and the Algebraic Stability of Persistence Barcodes
• Decomposition of pointwise finite-dimensional persistence modules
• 1-Dimensional intrinsic persistence of geodesic spaces
• On Vietoris–Rips complexes of ellipses
• Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold

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