An axiomatic treatment of Persistent Homology
Algebraic Topology
2024-10-10 v1
Abstract
We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of axioms.
Cite
@article{arxiv.2410.05617,
title = {An axiomatic treatment of Persistent Homology},
author = {Sergio Tsuyoshi Ura and Marco Contessoto and Alice Kimie Miwa Libardi},
journal= {arXiv preprint arXiv:2410.05617},
year = {2024}
}
Comments
19 pages, 2 appendix sections