Module-Level Versus Chain-Level Stabilisation In Multiparameter Persistence
Abstract
We compare two recent approaches to stabilising multiparameter persistence invariants: Bjerkevik's ε-pruning of persistence modules and the chain-level ε-pruning for the M-invariant of spectral systems. We prove these are not equivalent: the M-invariant M p,b n is a bigraded object depending on both birth and death downsets, while the homology module Hn is singly-graded. We exhibit explicit bifiltrations where the two approaches have different stability behaviour, and characterise the structural reason for this divergence. Our results clarify the relationship between module-theoretic and spectral-system approaches to multiparameter persistence.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Metabolomics and Mass Spectrometry Studies
Clusterin in disease pathology
Publication details
- Journal / source
- SSRN Electronic Journal
- Publisher
- Elsevier BV
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Preprint