Topological spaces of persistence modules and their properties
Algebraic Topology
2019-12-12 v2 General Topology
Abstract
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties.
Keywords
Cite
@article{arxiv.1802.08117,
title = {Topological spaces of persistence modules and their properties},
author = {Peter Bubenik and Tane Vergili},
journal= {arXiv preprint arXiv:1802.08117},
year = {2019}
}
Comments
32 pages, to appear in Journal of Applied and Computational Topology