Footprints of geodesics in persistent homology

DOI10.1007/s00009-022-02089-0OpenAlexW3138005094WikidataQ125757578 ScholiaQ125757578MaRDI QIDQ2148349

Žiga Virk

Publication date: 23 June 2022

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

Full work available at URL: https://arxiv.org/abs/2103.07158

zbMATH Keywords

persistent homologygeodesic spacelength geometry

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Geometric structures on manifolds of high or arbitrary dimension (57N16) Algebraic topology of manifolds (57N65) Abstract complexes in algebraic topology (55U05) Algebraic topology on manifolds and differential topology (57R19)

Related Items (8)

Rips complexes as nerves and a functorial Dowker-nerve diagram ⋮ Reconstruction properties of selective Rips complexes ⋮ Vietoris-Rips metric thickenings of the circle ⋮ The persistent topology of optimal transport based metric thickenings ⋮ Rigidity of terminal simplices in persistent homology ⋮ Critical edges in Rips complexes and persistence ⋮ Vietoris thickenings and complexes have isomorphic homotopy groups ⋮ Contractions in persistence and metric graphs

Uses Software

• GitHub
• Ripser

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A combinatorial approach to coarse geometry
• Persistence stability for geometric complexes
• The observable structure of persistence modules
• Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability
• Vietoris-Rips complexes of planar point sets
• Shape theory. An introduction
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• A complete characterization of the one-dimensional intrinsic Čech persistence diagrams for metric graphs
• Spectral theory in Riemannian geometry
• The Vietoris-Rips complexes of a circle
• Finding the homology of submanifolds with high confidence from random samples
• Rips complexes as nerves and a functorial Dowker-nerve diagram
• The length spectrum of Riemannian two-step nilmanifolds1
• Topological Data Analysis with Bregman Divergences
• 1-Dimensional intrinsic persistence of geodesic spaces
• On Vietoris–Rips complexes of ellipses
• Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
• Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold

This page was built for publication: Footprints of geodesics in persistent homology