A Survey on Applications of a New Approach to Quillen Rational Homotopy Theory

Recently, the classical Quillen approach to rational homotopy theory was extended to the non simply connected setting by means of a Quillen pair of adjoint functors between the categories of simplicial sets and complete differential graded Lie algebras. In this survey we present some applications, of this new approach. First we give an extension of the well know Baues-Lemaire conjecture, together with a short proof of this result. Then we describe how the new setting let us discover topological features hidden in the derivations of a given Lie algebra.