Ephemeral persistence modules and distance comparison

Berkouk, Nicolas; Petit, François

doi:10.2140/agt.2021.21.247

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Ephemeral persistence modules and distance comparison

Nicolas Berkouk and François Petit

Algebraic & Geometric Topology 21 (2021) 247–277

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.

Keywords

persistent homology, interleaving distance, sheaf theory

Mathematical Subject Classification 2010

Primary: 35A27, 55N99

Secondary: 18A99

References

Publication

Received: 26 June 2019

Revised: 26 April 2020

Accepted: 11 May 2020

Published: 25 February 2021

Authors

Nicolas Berkouk
Inria Saclay-Ile-de-France Palaiseau France

François Petit
Université de Paris CRESS, INSERM, INRA Paris France

Volume 21, issue 1 (2021)