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arXiv · 2403.06078

Decomposition of Persistent Homology and Spectral Sequences

Peiqi Yang·Yingfeng Hu·Hao Wu
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Abstract

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.

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Peiqi Yang, Yingfeng Hu, Hao Wu. 2024-03-10. Decomposition of Persistent Homology and Spectral Sequences. https://arxiv.org/abs/2403.06078

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