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Properties and Stability of Persistence Matching Diagrams

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arxiv 2409.14954 v2 pith:324ER2II submitted 2024-09-23 math.AT

Alvaro Torras-Casas , Rocio Gonzalez-Diaz This is my paper · ORCID
classification math.AT
keywords matchingpersistencediagramsembeddingsinducedstabilitymetricresult
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We introduce persistence matching diagrams induced by set mappings of metric spaces, based on 0-persistent homology of Vietoris-Rips filtrations. Also, we present a geometric definition of the persistence matching diagram that is more intuitive than the algebraic one. In addition, we show that such matching diagrams encapsulate the information of persistence morphism images, kernels and cokernels induced by embeddings. The main result is a stability theorem for persistence matching diagrams induced by embeddings. At the end, we adapt our stability result for set injections (not embeddings) of finite metric spaces.

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Cited by 1 Pith paper

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  1. Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack

    math.MG 2025-07 conditional novelty 6.0 of 10

    Introduces the C-constrained Gromov-Hausdorff distance for chromatic metric pairs and proves that all six diagrams in a six-pack are stable in bottleneck distance with respect to it, up to a factor of 2.

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