Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain

📝 Original Info

• Title: Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain
• ArXiv ID: 2511.07614
• Date: 2025-11-10
• Authors: ** 정보 없음 (제공된 텍스트에 저자 정보가 포함되어 있지 않음) **

📝 Abstract

We study pointwise free and finitely-generated persistence modules over a principal ideal domain, indexed by a (possibly infinite) totally-ordered poset category. We show that such persistence modules admit interval decompositions if and only if every structure map has free cokernel. We also show that, in torsion-free settings, the integer persistent homology module of a filtration of topological spaces admits an interval decomposition if and only if the associated persistence diagram is invariant to the choice of coefficient field. These results generalize prior work where the indexing category is finite.

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