THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES

Chazal F, Crawley-Boevey WW, de Silva V (2016)
HOMOLOGY HOMOTOPY AND APPLICATIONS 18(2): 247-265.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
HOMOLOGY HOMOTOPY AND APPLICATIONS
Band
18
Ausgabe
2
Seite(n)
247-265
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Chazal F, Crawley-Boevey WW, de Silva V. THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY HOMOTOPY AND APPLICATIONS. 2016;18(2):247-265.
Chazal, F., Crawley-Boevey, W. W., & de Silva, V. (2016). THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY HOMOTOPY AND APPLICATIONS, 18(2), 247-265. doi:10.4310/HHA.2016.v18.n2.a14
Chazal, F., Crawley-Boevey, W. W., and de Silva, V. (2016). THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY HOMOTOPY AND APPLICATIONS 18, 247-265.
Chazal, F., Crawley-Boevey, W.W., & de Silva, V., 2016. THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY HOMOTOPY AND APPLICATIONS, 18(2), p 247-265.
F. Chazal, W.W. Crawley-Boevey, and V. de Silva, “THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES”, HOMOLOGY HOMOTOPY AND APPLICATIONS, vol. 18, 2016, pp. 247-265.
Chazal, F., Crawley-Boevey, W.W., de Silva, V.: THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES. HOMOLOGY HOMOTOPY AND APPLICATIONS. 18, 247-265 (2016).
Chazal, Frederic, Crawley-Boevey, William Walstan, and de Silva, Vin. “THE OBSERVABLE STRUCTURE OF PERSISTENCE MODULES”. HOMOLOGY HOMOTOPY AND APPLICATIONS 18.2 (2016): 247-265.