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arXiv · 2303.14694

A stability theorem for bigraded persistence barcodes

Anthony Bahri·Ivan Limonchenko·Taras Panov·Jongbaek Song·Donald Stanley
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Abstract

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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Anthony Bahri, Ivan Limonchenko, Taras Panov, Jongbaek Song, Donald Stanley. 2023-03-26. A stability theorem for bigraded persistence barcodes. https://doi.org/10.1007/s00454-025-00771-0

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