I have uploaded a new preprint, The Lambrechts–Stanley Model of Configuration Spaces, which you can find on arXiv. Here is the abstract:
We prove the validity over ℝ of a CDGA model of configuration spaces for simply connected manifolds with vanishing Euler characteristic, 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, 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 manifolds.
I would of course be interested in any comment, question… about this paper.