Interval decomposition of infinite persistence modules over a principal ideal domain and field choice in persistent homology
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.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Homotopy and Cohomology in Algebraic Topology
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4931–4945
- Publication date
- 24 April 2026
- Language
- EN