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A stability theorem for bigraded persistence barcodes

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arxiv 2303.14694 v3 pith:7X3TYNHP submitted 2023-03-26 math.AT cs.CGcs.LGmath.COmath.MG

Anthony Bahri , Ivan Limonchenko , Taras Panov , Jongbaek Song , Donald Stanley This is my paper · ORCID
classification math.ATcs.CGcs.LGmath.COmath.MG
keywords bigradedbarcodeshomologydoublemodulespersistentstabilitytheorem
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We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes.

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  1. Algebraic interleavings of spaces over the classifying space of the circle

    math.AT 2025-01 accept novelty 6.0 of 10

    A new cohomological interleaving distance for spaces over BS^1 is shown to equal the homotopy interleaving distances of Blumberg-Lesnick and Lanari-Scoccola, and is computed via barcodes for CP^n and rational homotopy...

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