Article Dans Une Revue Homology, Homotopy and Applications Année : 2026

Local characterization of block-decomposability for multiparameter persistence modules

Résumé

Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the class of indecomposables called block modules, which plays a prominent role in levelset persistence. Here we generalize the local condition for decomposability into block modules to the n-parameter setting, and prove a corresponding structure theorem. Our result holds in the generality of pointwise finite-dimensional modules over finite products of arbitrary totally ordered sets. Our proof extends the one by Botnan and Crawley-Boevey from 2 to n parameters, which requires some crucial adaptations at places where their proof is fundamentally tied to the 2-parameter setting.

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hal-05026629 , version 1 (09-04-2025)

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Vadim Lebovici, Jan-Paul Lerch, Steve Oudot. Local characterization of block-decomposability for multiparameter persistence modules. Homology, Homotopy and Applications, 2026, 28 (1), pp.175-196. ⟨10.4310/HHA.2026.v28.n1.a9⟩. ⟨hal-05026629⟩
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