Computing Persistence Diagram Bundles
Algebraic Topology
2023-09-21 v2 Computational Geometry
Abstract
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space . In this paper, we present an algorithm for computing piecewise-linear PD bundles, a wide class that includes many of the PD bundles that one may encounter in practice. Full details are given for the case in which is a triangulated surface, and we outline the generalization to higher dimensions and other cases.
Cite
@article{arxiv.2210.06424,
title = {Computing Persistence Diagram Bundles},
author = {Abigail Hickok},
journal= {arXiv preprint arXiv:2210.06424},
year = {2023}
}
Comments
21 pages, 8 figures. Expository changes throughout