Rational Homotopy Equivalence

TL;DR

This paper introduces an algorithm to construct Sullivan minimal models for simply connected simplicial sets with effective homology, enabling the decision of rational homotopy equivalence between such spaces.

Contribution

It presents a novel algorithmic method to determine rational homotopy type for simply connected spaces represented by finite simplicial sets.

Findings

Algorithm successfully constructs Sullivan minimal models

Decides rational homotopy equivalence algorithmically

Applicable to spaces with effective homology

Abstract

This article proposes an algorithm that constructs a Sullivan minimal model for any simply connected simplicial set with effective homology and thereby allows one to decide algorithmically whether two simply connected spaces represented by finite simplicial sets have the same rational homotopy type.