A stability theorem for bigraded persistence barcodes

arXiv:2303.14694v2 Announce Type: replace-cross
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.

abstract arxiv cs.cg cs.lg math.at math.co math.mg modules ordinary persistence prove space stability theorem type