Lower bounds on the homology of Vietoris-Rips complexes of hypercube graphs

DOI10.1007/s40840-024-01663-xarXiv2309.06222OpenAlexW4392377833MaRDI QIDQ6196815

Žiga Virk, Henry Adams

Publication date: 15 March 2024

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/2309.06222

zbMATH Keywords

clique complexeshypercubesBetti numbersVietoris-Rips complexes

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Simplicial sets and complexes in algebraic topology (55U10) Combinatorial aspects of simplicial complexes (05E45)

Cites Work

• Ripser: efficient computation of Vietoris-Rips persistence barcodes
• Nerve complexes of circular arcs
• Clique complexes and graph powers
• Persistence stability for geometric complexes
• A complete characterization of the one-dimensional intrinsic Čech persistence diagrams for metric graphs
• Contractions in persistence and metric graphs
• On Vietoris-Rips complexes of hypercube graphs
• Persistent homology of the sum metric
• The Vietoris-Rips complexes of a circle
• Rips complexes as nerves and a functorial Dowker-nerve diagram
• Topology and data
• 1-Dimensional intrinsic persistence of geodesic spaces
• Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold
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