Bottleneck Stability for Generalized Persistence Diagrams

TL;DR

This paper extends the concept of bottleneck stability to one-dimensional constructible persistence modules valued in any small abelian category, broadening the applicability of stability results in topological data analysis.

Contribution

It introduces a generalized stability framework for persistence diagrams in a broader categorical setting, enhancing theoretical understanding.

Findings

Bottleneck stability is extended to new categorical contexts.

The framework applies to a wide class of persistence modules.

The results generalize existing stability theorems.

Abstract

In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.