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Homological properties of persistent homology

Varli, Hanife; Pamuk, Mehmetcik; Yilmaz, Yagmur


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        "affiliation": "Cankiri Karatekin Univ, Dept Math, TR-18100 Cankiri, Turkiye", 
        "name": "Varli, Hanife"
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        "affiliation": "Middle East Tech Univ, Dept Math, TR-06531 Ankara, Turkiye", 
        "name": "Pamuk, Mehmetcik"
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        "affiliation": "Univ Toledo, Dept Math & Stat, Toledo, OH USA", 
        "name": "Yilmaz, Yagmur"
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    "description": "<p>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.</p>", 
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