A stability theorem for bigraded persistence barcodes
Algebraic Topology
2025-09-09 v3 Computational Geometry
Machine Learning
Combinatorics
Metric Geometry
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.
Cite
@article{arxiv.2303.14694,
title = {A stability theorem for bigraded persistence barcodes},
author = {Anthony Bahri and Ivan Limonchenko and Taras Panov and Jongbaek Song and Donald Stanley},
journal= {arXiv preprint arXiv:2303.14694},
year = {2025}
}
Comments
22 pages, published version