Answers are grounded in this paper and cite their sources.
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.
No takes yet. Share an insight, caveat, or question.
Yang et al. (2024) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: