Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules

Isabella Mastroianni; Marco Guerra; Ulderico Fugacci; Emanuela De Negri

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arXiv · 2506.14678

Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules

Isabella Mastroianni·Marco Guerra·Ulderico Fugacci·Emanuela De Negri

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Abstract

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.

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Isabella Mastroianni, Marco Guerra, Ulderico Fugacci, Emanuela De Negri. 2025-06-17. Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules. https://arxiv.org/abs/2506.14678

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