Local characterizations for decomposability of 2-parameter persistence modules - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Algebras and Representation Theory Année : 2023

Local characterizations for decomposability of 2-parameter persistence modules

Résumé

We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.
Fichier principal
Vignette du fichier
main.pdf (960.39 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02995822 , version 1 (30-01-2023)

Licence

Paternité

Identifiants

Citer

Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot. Local characterizations for decomposability of 2-parameter persistence modules. Algebras and Representation Theory, 2023, ⟨10.1007/s10468-022-10189-4⟩. ⟨hal-02995822⟩
50 Consultations
31 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More