Ladder Decomposition for Morphisms of Persistence Modules

Giansiracusa, Jeffrey; Urbančič, Živa

Abstract

The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described entirely by the barcode invariant. In this paper we investigate when a morphism Φ:V→W of persistence modules admits an analogous direct sum decomposition. Jacquard et al. showed that a ladder decomposition can be obtained whenever the barcodes of V and W do not have any strictly nested bars. We refine this result and show that even in the presence of nested bars, a ladder decomposition exists when the morphism is sufficiently close to being invertible relative to the scale of the nested bars.

Citation

Giansiracusa, J., & Urbančič, Ž. (2024). Ladder Decomposition for Morphisms of Persistence Modules. Journal of Applied and Computational Topology, 8, 2069–2109. https://doi.org/10.1007/s41468-024-00174-9

• Journal Article Type: Article
• Acceptance Date: Apr 8, 2024
• Online Publication Date: May 10, 2024
• Publication Date: 2024-11
• Deposit Date: Apr 26, 2024
• Publicly Available Date: May 10, 2024
• Journal: Journal of Applied and Computational Topology
• Print ISSN: 2367-1726
• Electronic ISSN: 2367-1734
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Pages: 2069–2109
• DOI: https://doi.org/10.1007/s41468-024-00174-9
• Public URL: https://durham-repository.worktribe.com/output/2397266