Sullivan minimal model

Summary

A Sullivan minimal model is a free graded-commutative differential graded algebra over $\Q$ with a decomposable differential. It models the rational homotopy type of a space. Every simply connected space of finite type has a minimal model, unique up to isomorphism. Its generators in degree $n$ form the dual of the rational homotopy group $\pi_n(X) \otimes \Q$, and its cohomology is the rational cohomology of $X$. So the minimal model is the main computational tool of rational homotopy theory.