Geodesic
The observable structure of persistence modules
Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 247-265.

Voir la notice de l'article provenant de la source International Press of Boston

In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered finite set or the natural numbers, such diagrams do not provide a complete invariant of q-tame modules. The purpose of this paper is to show that the category of persistence modules can be adjusted to overcome this issue. We introduce the observable category of persistence modules: a localization of the usual category, in which the classical properties of q-tame modules still hold but where the persistence diagram is a complete isomorphism invariant and all q-tame modules admit an interval decomposition.
DOI : 10.4310/HHA.2016.v18.n2.a14
Classification : 55U99
Keywords: persistence module, persistent homology 
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Frédéric Chazal; William Crawley-Boevey; Vin de Silva. The observable structure of persistence modules. Homology, homotopy, and applications, Tome 18 (2016) no. 2, pp. 247-265. doi : 10.4310/HHA.2016.v18.n2.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n2.a14/

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