The observable structure of persistence modules

By Frédéric Chazal, W. Crawley‐Boevey, Vin de Silva. 2014

58 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/6843752ca46ea00893a339638a524212b47f1f82

Citations in the corpus

• Wasserstein Stability for Persistence Diagrams (2020, unknown): “Linear representations of persistence diagrams are a common form of topological summaries.”