Cell decompositions of persistent minimal models

Abstract

In this article we generalize the main structure theorems of rational homotopy theory to the persistent setting. Our main motivation is the computation of an explicit finite, cellular presentation of the persistent minimal model that completely characterizes the rational homotopy type of copersistent simply-connected spaces. We achieve this via an explicit construction of the minimal model of a tame persistent CDGA as an iterated sequence of cell attachments. As an application of our results, we construct an explicit decomposition of the rational Postnikov tower of simply-connected copersistent spaces in terms of a tower of persistent Eilenberg-Maclane intervals