Persistence Minimal Free Lie Model

TL;DR

This paper introduces the persistence minimal Quillen model, integrating rational homotopy theory and persistence modules to provide a refined algebraic framework for topological data analysis with proven stability.

Contribution

It develops a novel algebraic model combining rational homotopy theory and persistence modules, enhancing the analysis of topological data with stability guarantees.

Findings

Constructed the persistence minimal Quillen model.

Provided stability results for the model.

Offers a refined approach over traditional homology computations.

Abstract

The minimal Quillen model is a free Lie model for rational spaces proposed by Quillen. Meanwhile, persistence modules are theoretical abstractions of persistent homology. In this paper, we integrate the ideas of rational homotopy theory and persistence modules to construct the persistence minimal Quillen model and discuss its stability. Our results provide a new algebraic framework for topological data analysis, which is more refined compared to directly computing the homology groups of the filtration of simplicial complexes. Furthermore, the stability results for persistence minimal Lie models ensure that our model is well-founded.