Homological properties of persistent homology

Date

2024-01-01

Author

Varll, Hanife
Pamuk, Mehmetcik
Yilmaz, Yaǧmur

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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.

Subject Keywords

Mayer-Vietoris sequence, Perfect discrete Morse function, persistent module, relative pair

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85210403100&origin=inward
https://hdl.handle.net/11511/112823

Journal

Journal of Algebra and its Applications

DOI

https://doi.org/10.1142/s0219498826500374

Collections

Department of Mathematics, Article

Citation Formats

H. Varll, M. Pamuk, and Y. Yilmaz, “Homological properties of persistent homology,” Journal of Algebra and its Applications, pp. 0–0, 2024, Accessed: 00, 2024. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85210403100&origin=inward.