Conference for Young researchers in homotopy theory and categorical structures @ Max Planck Institute for Mathematics (MPIM Bonn)

We prove the validity over ℝ of a CDGA model of configuration spaces for simply connected manifolds of dimension at least 4, answering a conjecture of Lambrechts--Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on a Poincaré duality model of the manifold. We moreover prove that our model is compatible with the action of the Fulton--MacPherson operad when the manifold is framed, by relying on Kontsevich’s proof of the formality of the little disks operads. We use this more precise result to get a complex computing factorization homology of framed manifolds.