Homological properties of persistent homology

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Varll H., Pamuk M., Yilmaz Y.

Journal of Algebra and its Applications, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • 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
  • 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.