# Decomposition of exact pfd persistence bimodules

1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We identify a certain class of persistence modules indexed over $\mathbb{R}^2$ that are decomposable into direct sums of indecomposable summands called blocks. The conditions on the modules are that they are both pointwise finite-dimensional (pfd) and exact. Our proof follows the same scheme as the one for pfd persistence modules indexed over $\mathbb{R}$, yet it departs from it at key stages due to the product order not being a total order on $\mathbb{R}^2$, which leaves some important gaps open. These gaps are filled in using more direct arguments. Our work is motivated primarily by the study of interlevel-sets persistence, although the proposed results reach beyond that setting.
Type de document :
Pré-publication, Document de travail
2016
Domaine :

https://hal.inria.fr/hal-01359312
Contributeur : Steve Oudot <>
Soumis le : vendredi 2 septembre 2016 - 10:53:22
Dernière modification le : mardi 17 avril 2018 - 09:08:37

### Identifiants

• HAL Id : hal-01359312, version 1
• ARXIV : 1605.09726

### Citation

Cochoy Jérémy, Steve Y. Oudot. Decomposition of exact pfd persistence bimodules. 2016. 〈hal-01359312〉

### Métriques

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