A stability theorem for bigraded persistence barcodes

Published 26 Mar 2023 in math.AT, cs.CG, cs.LG, math.CO, and math.MG | (2303.14694v2)

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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