Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911404763643904 |
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| author | Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela |
| author_facet | Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela |
| contents | Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of product between two monoparameter persistence modules. While originally conceived to serve this comparative purpose, our construction unexpectedly reveals a deeper structural property: it also characterizes a class of biparameter modules known as hook-decomposable modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela Algebraic Topology Commutative Algebra Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of product between two monoparameter persistence modules. While originally conceived to serve this comparative purpose, our construction unexpectedly reveals a deeper structural property: it also characterizes a class of biparameter modules known as hook-decomposable modules. |
| title | Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules |
| topic | Algebraic Topology Commutative Algebra |
| url | https://arxiv.org/abs/2506.14678 |