Hausdorff stability of persistence spaces

DOI10.1007/s10208-015-9244-1zbMath1358.55005OpenAlexW2064704056MaRDI QIDQ285432

Andrea Cerri, Landi, Claudia

Publication date: 19 May 2016

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-015-9244-1

zbMATH Keywords

multiplicityhomological critical valuemultidimensional persistencepersistent Betti numbers

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Homology and cohomology theories in algebraic topology (55N99)

Related Items (4)

Computing multiparameter persistent homology through a discrete Morse-based approach ⋮ Rigorous cubical approximation and persistent homology of continuous functions ⋮ On the geometrical properties of the coherent matching distance in 2D persistent homology ⋮ Morse-based fibering of the persistence rank invariant

Cites Work

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• Comparison of persistent homologies for vector functions: from continuous to discrete and back
• Stability of persistence diagrams
• The theory of multidimensional persistence
• Size homotopy groups for computation of natural size distances
• Betti numbers in multidimensional persistent homology are stable functions
• One-dimensional reduction of multidimensional persistent homology
• The Persistence Space in Multidimensional Persistent Homology
• Necessary conditions for discontinuities of multidimensional persistent Betti numbers
• Proximity of persistence modules and their diagrams
• PERSISTENCE BARCODES FOR SHAPES
• Size functions and formal series

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