Sullivan completions

Abstract

The Sullivan construction associates to each path connected space or connected simplicial set, $X$, a special cdga, its minimal model $(\land V,d)$, and to each such cdga $\land W$ its geometric realisation $\langle \land W\rangle$. The composite of these constructions is the Sullivan completion, $X_{\mathbb Q}$, of $X$. In this paper we give a survey of the main properties of Sullivan completions, and include explicit examples.