Abstract

The rational homotopy theory of spaces is the study of topological spaces modulo torsion. The rational homotopy of a space is determined by two dual algebraic models: the Sullivan model, defined by a commutative dg-algebra structure, and the Quillen model, defined by a Lie dg-algebra.

Furthermore, each space has a minimal Sullivan model, which can be used to prove that the rational homotopy automorphisms of a space form an algebraic group, with a deformation complex of the Sullivan model as Lie algebra. The purpose of this lecture is to provide a survey of these results, after short recollections on the definition of the Sullivan model of a space.

General reference: B. Fresse, “Homotopy of operads and Grothendieck-Teichmller Groups”. Book project. First volume available on the web-page “http://math.univ-lille1.fr/%7Efresse/OperadGT-December2012Preprint.pdf”