An axiomatic treatment of Persistent Homology
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917796543201280 |
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| author | Ura, Sergio Tsuyoshi Contessoto, Marco Libardi, Alice Kimie Miwa |
| author_facet | Ura, Sergio Tsuyoshi Contessoto, Marco Libardi, Alice Kimie Miwa |
| contents | We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of axioms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An axiomatic treatment of Persistent Homology Ura, Sergio Tsuyoshi Contessoto, Marco Libardi, Alice Kimie Miwa Algebraic Topology 55N31, 55N20, 55N40, 55U99 We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of axioms. |
| title | An axiomatic treatment of Persistent Homology |
| topic | Algebraic Topology 55N31, 55N20, 55N40, 55U99 |
| url | https://arxiv.org/abs/2410.05617 |