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<p>We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space <i>X</i> using the ordinary and double homology of the moment-angle complex associated with the Vietoris–Rips filtration of&#xa0;<i>X</i>. We prove a stability theorem for the bigraded persistent double homology modules and barcodes.</p>

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A Stability Theorem for Bigraded Persistence Barcodes

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Anthony Bahri,
  • Ivan Limonchenko,
  • Taras Panov,
  • Jongbaek Song,
  • Donald Stanley

摘要

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.