[en] We provide a definition of ephemeral multi-persistent modules and prove that the quotient 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.
Disciplines :
Mathematics
Author, co-author :
Berkouk, Nicolas
Petit, François ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Ephemeral persistence modules and distance comparison