The observable structure of persistence modules
type: Dataset
description: 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.
issued: 2026-05-05T10:11:17.701175
language: en
modified: 2026-05-05T10:11:17.701180
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-rtmathematics-mathrepresentation-theory-mathrt
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00996720

The observable structure of persistence modules
type: Distribution
format: HTML
issued: 2026-05-05T10:11:17.702532
modified: 2026-05-05T10:11:17.695655
access URL: https://hal.science/hal-00996720

test_moissonnage_selune
type: Agent