Homological properties of persistent homology
Journal of Algebra and its Applications, vol.25, no.6, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 25 Issue: 6
- Publication Date: 2026
- Doi Number: 10.1142/s0219498826500374
- Journal Name: Journal of Algebra and its Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Keywords: Mayer–Vietoris sequence, Perfect discrete Morse function, persistent module, relative pair
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
Abstract
In this paper, we investigate to what extent persistent homology benefits from the properties of a homology theory. We show that persistent homology benefits from a Mayer-Vietoris sequence and a long exact sequence for a pair if one works with graded persistence modules. We also give concrete examples showing that the same is not the case for persistent homology groups.