Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
Algebraic Topology
2026-01-30 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.2506.14678,
title = {Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules},
author = {Isabella Mastroianni and Marco Guerra and Ulderico Fugacci and Emanuela De Negri},
journal= {arXiv preprint arXiv:2506.14678},
year = {2026}
}