Mario Fuentes: Lie models of classifying fibrations

Abstract.

The universal fibration sequence, \(X\to B\text{aut}^*(X)\to B\text{aut}(X)\), classifies those fibration sequences whose fiber is of the homotopy type of a given space X. This is a central object in Algebraic Topology, and our goal is to study it from the perspective of Rational Homotopy Theory.

A well-known result is the Quillen model of the simply connected covering of the universal fibration, for X that is simply connected. However, this double restriction to the simply-connected setting is imposed by the use of the Quillen approach to Rational Homotopy Theory. To address non-simply-connected spaces, we propose a new approach based on complete Lie algebras, which allows us to generalize the classical results in this field.