Translator Disclaimer
2021 Ephemeral persistence modules and distance comparison
Nicolas Berkouk, François Petit
Algebr. Geom. Topol. 21(1): 247-277 (2021). DOI: 10.2140/agt.2021.21.247

Abstract

We provide a definition of ephemeral multipersistent modules and prove that the quotient category of persistent modules by the ephemeral ones is equivalent to the category of γ–sheaves. In the case of one-dimensional persistence, our definition agrees with the usual one, showing that the observable category and the category of γ–sheaves are equivalent. We also establish isometry theorems between the category of persistent modules and γ–sheaves both endowed with their interleaving distance. Finally, we compare the interleaving and convolution distances.

Citation

Download Citation

Nicolas Berkouk. François Petit. "Ephemeral persistence modules and distance comparison." Algebr. Geom. Topol. 21 (1) 247 - 277, 2021. https://doi.org/10.2140/agt.2021.21.247

Information

Received: 26 June 2019; Revised: 26 April 2020; Accepted: 11 May 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.247

Subjects:
Primary: 35A27, 55N99
Secondary: 18A99

Rights: Copyright © 2021 Mathematical Sciences Publishers

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.21 • No. 1 • 2021
MSP
Back to Top