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.

翻译：我们使用动量角复合体的普通和双重同调来定义有限赝度量空间 X 的双分级持久同调模和双分级条形码。我们证明了双分级持久双同调模和条形码的稳定性定理。