Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911561535193088 |
|---|---|
| author | Luo, Jiajie Henselman-Petrusek, Gregory |
| author_facet | Luo, Jiajie Henselman-Petrusek, Gregory |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology Luo, Jiajie Henselman-Petrusek, Gregory Algebraic Topology Computational Geometry Category Theory 62R40, 55N31, 55-08 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. |
| title | Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology |
| topic | Algebraic Topology Computational Geometry Category Theory 62R40, 55N31, 55-08 |
| url | https://arxiv.org/abs/2511.07614 |