Decomposition of Persistent Homology and Spectral Sequences
Algebraic Topology
2024-03-25 v2
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.
Cite
@article{arxiv.2403.06078,
title = {Decomposition of Persistent Homology and Spectral Sequences},
author = {Peiqi Yang and Yingfeng Hu and Hao Wu},
journal= {arXiv preprint arXiv:2403.06078},
year = {2024}
}