Directed homology and persistence modules

Eric Goubault

doi:10.1007/s41468-024-00197-2

Directed homology and persistence modules

Eric Goubault

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We give a mostly self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistent homology and natural homology. We study its first properties, among which are relative homology and Mayer–Vietoris long exact sequences and a Künneth formula.

Original language	English
Article number	3
Journal	Journal of Applied and Computational Topology
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s41468-024-00197-2
Publication status	Published - 1 Mar 2025

Keywords

Directed topology
Natural homology
Persistent homology

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10.1007/s41468-024-00197-2

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title = "Directed homology and persistence modules",

abstract = "We give a mostly self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistent homology and natural homology. We study its first properties, among which are relative homology and Mayer{\textendash}Vietoris long exact sequences and a K{\"u}nneth formula.",

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KW - Directed topology

KW - Natural homology

KW - Persistent homology

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Directed homology and persistence modules

Abstract

Keywords

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