Journal
HOMOLOGY HOMOTOPY AND APPLICATIONS
Volume 18, Issue 2, Pages 247-265Publisher
INT PRESS BOSTON, INC
DOI: 10.4310/HHA.2016.v18.n2.a14
Keywords
persistence module; persistent homology
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Funding
- French ANR [TopData ANR-13-BS01-0008]
- Simons Foundation [267571]
- National Science Foundation
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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.
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