Decomposition of Persistent Homology and Spectral Sequences

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 informat...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Yang, Peiqi, Hu, Yingfeng, Wu, Hao
Format: Article
Language:English
Subjects:
Decomposition
Homology
Online Access:Get full text
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Summary: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.
ISSN:2331-8422