# Mario Fuentes: Lie models of classifying fibrations

**Time: **
Tue 2023-03-28 11.00 - 12.00

**Location: **
Cramer room, Albano

**Participating: **
Mario Fuentes (Malaga)

**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.