Finiteness of rank invariants of multidimensional persistent homology groups

DOI10.1016/j.aml.2010.11.004zbMath1206.55008arXiv1001.0358OpenAlexW2963070799WikidataQ59442779 ScholiaQ59442779MaRDI QIDQ617024

Francesca Cagliari, Landi, Claudia

Publication date: 20 January 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0358

zbMATH Keywords

Betti numbersshape analysisEuclidean neighborhood retractpersistent topology

Mathematics Subject Classification ID

Related Items (8)

Euler characteristic surfaces ⋮ Stable comparison of multidimensional persistent homology groups with torsion ⋮ Fractal dimension estimation with persistent homology: a comparative study ⋮ Comparison of persistent homologies for vector functions: from continuous to discrete and back ⋮ Parametrized homology via zigzag persistence ⋮ Necessary conditions for discontinuities of multidimensional persistent Betti numbers ⋮ A brief introduction to multidimensional persistent Betti numbers ⋮ G -invariant persistent homology

Cites Work

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• Stability of persistence diagrams
• The theory of multidimensional persistence
• Betti numbers in multidimensional persistent homology are stable functions
• One-dimensional reduction of multidimensional persistent homology
• Topology and data
• Proximity of persistence modules and their diagrams
• On the Kunneth Formula and Functorial Dependence in Algebraic Topology

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