Decomposition of Persistent Homology and Spectral Sequences

2024/03/10 by Peiqi Yang, Ying Hu, Yang, Peiqi +3
Computer Science · Mathematics · #55N31 #55T05 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2403.06078

openalex publication_date 2024/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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