Directed Homology and Persistence Modules

2023/09/13 by Éric Goubault, Goubault, Eric · 1 citation
Computer Science · Engineering · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Algorithm #Amino acid #Biology #Computational biology #Engineering #FOS: Mathematics #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Persistence (discontinuity) #Persistent homology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2309.07095

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some exact sequences.

Cited by

• Directed homotopy modules

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