Chazal, F, Crawley-Boevey, WW and de Silva, V (2016) The observable structure of persistence modules. Homology, Homotopy and Applications, 18 (2). pp. 247-265. ISSN 1532-0073
Abstract
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 de- finable. 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of a paper accepted for publication in Homology, Homotopy and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Persistence module, Persistent homology |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Feb 2016 12:23 |
Last Modified: | 11 Apr 2017 15:15 |
Published Version: | https://doi.org/10.4310/HHA.2016.v18.n2.a14 |
Status: | Published |
Publisher: | International Press |
Identification Number: | 10.4310/HHA.2016.v18.n2.a14 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94496 |