GDO

Abstract

The purpose of this talk is to give a description of the set of homotopy classes of formality quasi-isomorphisms for a Sullivan model of the Little n-discs operads, where we consider any n>1.

The Sullivan model of a topological operad combines a commutative dg-algebra structure, reflecting the rational homotopy of the spaces underlying the operad, and a cooperad structure, reflecting the composition structures of the operad. I will explain the definition of an obstruction spectral sequence for the formality of these Sullivan models of operads.

I will give a description of the obstruction spectral sequence associated to the little discs operads, and I will explain the connection with the definition of the Drinfeld associators.