Ladder Decomposition for Morphisms of Persistence Modules

Giansiracusa, Jeffrey; Urbancic, Ziva

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., & Urbancic, Z. (in press). Ladder Decomposition for Morphisms of Persistence Modules. Journal of Applied and Computational Topology,

• Journal Article Type: Article
• Acceptance Date: Apr 8, 2024
• Deposit Date: Apr 26, 2024
• Journal: Journal of Applied and Computational Topology
• Print ISSN: 2367-1726
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Public URL: https://durham-repository.worktribe.com/output/2397266
• Publisher URL: https://link.springer.com/journal/41468