An algorithm to compute minimal Sullivan algebras

TL;DR

This paper presents an algorithm that transforms a given Sullivan algebra into its minimal model, enabling efficient computation of rational cohomology and related topological invariants.

Contribution

It introduces a modified AT-model algorithm tailored for Sullivan algebras to compute minimal models from non-minimal ones.

Findings

Algorithm successfully computes minimal Sullivan models

Preserves rational cohomology during transformation

Applicable to finite Sullivan algebras with ordered generators

Abstract

In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a kind of modified AT-model algorithm used to compute in the past other kinds of topology information such as (co)homology, cup products on cohomology and persistent homology. Taking as input a (non-minimal) Sullivan algebra $A$ with an ordered finite set of generators preserving the filtration defined on $A$, we obtain as output a minimal Sullivan algebra with the same rational cohomology as $A$.