Published January 1, 2024
| Version v1
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Homological properties of persistent homology
- 1. Cankiri Karatekin Univ, Dept Math, TR-18100 Cankiri, Turkiye
- 2. Middle East Tech Univ, Dept Math, TR-06531 Ankara, Turkiye
- 3. Univ Toledo, Dept Math & Stat, Toledo, OH USA
Description
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.
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