Decomposition of Persistent Homology and Spectral Sequences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916170802659328 |
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| author | Yang, Peiqi Hu, Yingfeng Wu, Hao |
| author_facet | Yang, Peiqi Hu, Yingfeng Wu, Hao |
| contents | We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general assumptions, these two algebraic structures capture the same information from the filtered chain complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decomposition of Persistent Homology and Spectral Sequences Yang, Peiqi Hu, Yingfeng Wu, Hao Algebraic Topology 55N31, 55T05 We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general assumptions, these two algebraic structures capture the same information from the filtered chain complex. |
| title | Decomposition of Persistent Homology and Spectral Sequences |
| topic | Algebraic Topology 55N31, 55T05 |
| url | https://arxiv.org/abs/2403.06078 |