A stability theorem for bigraded persistence barcodes

03/26/2023

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by   Anthony Bahri, et al.

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We define the bigraded persistent homology modules and the 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 the stability theorem for the bigraded persistent double homology modules and barcodes.