Algebraic stability theorem for derived categories of zigzag persistence modules

Yasuaki Hiraoka, Michio Yoshiwaki

Published 2020-06-12Version 1

The interleaving and bottleneck distances between ordinary persistence modules can be extended to the derived setting. Using these distances, we prove an algebraic stability theorem in the derived category of ordinary persistence modules. It is well known that the derived categories of ordinary and arbitrary zigzag persistence modules are equivalent. Through this derived equivalence, these distances can also be defined on the derived category of arbitrary zigzag persistence modules, and the algebraic stability theorem holds even in this setting. As a consequence, an algebraic stability theorem for arbitrary zigzag persistence modules is proved.