English

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.

Keywords

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