André–Quillen cohomology and rational homotopy of function spaces

• DOI: 10.1016/j.aim.2004.04.014
• Publication Date: 2004-06-29T12:32:30Z
• Authors: J. Block; A. Lazarev
• Keywords: Cofibration

We develop a simple theory of Andr��-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent $CW$-complexes. This puts certain results of Sullivan in a more conceptual framework.