PreprintCC BY 4.0arXiv
A result of continuous stability for generalized persistence diagrams
Abstract
We study persistence modules obtained from the A-fundamental groupoids of finite graphs. Moreover, we verify the categorical properties needed to form generalized persistence diagrams, and describe a quotient that identifies equivalent groupoids. A normalized linear presheaf construction places these modules in an essentially small abelian category, where Patel's Continuity Theorem gives a $1$-Lipschitz estimate in erosion distance. Explicit graph filtrations illustrate the groupoid-valued construction, and so we suggest a new approach to interpret persistence diagrams and large data sets in topological data analysis, based on recent works of A-homotopy theory of the last years.
Related
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BibTeX
@misc{bavuma2026result,
title = {{A result of continuous stability for generalized persistence diagrams}},
author = {Yanga Bavuma and Martin Mijangos and Francesco G. Russo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00799},
eprint = {2611.00799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A result of continuous stability for generalized persistence diagrams
AU - Yanga Bavuma
AU - Martin Mijangos
AU - Francesco G. Russo
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00799
UR - https://arxiv.org/abs/2611.00799
AB - We study persistence modules obtained from the A-fundamental groupoids of finite graphs. Moreover, we verify the categorical properties needed to form generalized persistence diagrams, and describe a quotient that identifies equivalent groupoids. A normalized linear presheaf construction places these modules in an essentially small abelian category, where Patel's Continuity Theorem gives a $1$-Lipschitz estimate in erosion distance. Explicit graph filtrations illustrate the groupoid-valued construction, and so we suggest a new approach to interpret persistence diagrams and large data sets in topological data analysis, based on recent works of A-homotopy theory of the last years.
ER -