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Mathematics > Algebraic Topology

Title: A stability theorem for bigraded persistence barcodes

Authors: Anthony Bahri, Ivan Limonchenko, Taras Panov, Jongbaek Song, Donald Stanley
(Submitted on 26 Mar 2023 (v1), last revised 28 Mar 2024 (this version, v2))
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.
Comments: 20 pages
Subjects: Algebraic Topology (math.AT); Computational Geometry (cs.CG); Machine Learning (cs.LG); Combinatorics (math.CO); Metric Geometry (math.MG)
MSC classes: Primary 57S12, 55N31, 57Z25, Secondary 13F55, 55U10
Cite as: arXiv:2303.14694 [math.AT]
  (or arXiv:2303.14694v2 [math.AT] for this version)

Submission history

From: Taras Panov [view email]
[v1] Sun, 26 Mar 2023 11:43:29 GMT (57kb,D)
[v2] Thu, 28 Mar 2024 16:37:06 GMT (58kb,D)
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