Cohomology of configuration space of a compact manifold There is a reference or a methode which by it we can calculate the cohomology of a configuration space of a compact manifold simply connected? It is possible to find a spectral sequence converging to this cohomology (but the Cohen-Taylor spectral sequence)?
 A: Shameless promotion ahead. If you are interested in cohomology with base field $\mathbb{R}$, then:


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*For simply connected manifolds without boundary you have my paper and a paper of Campos and Willwacher. Both papers give so-called "real models" for the configuration spaces; these models are commutative differential graded algebras, and in particular the cohomology of the model is the cohomology of the configuration space. 

*For simply connected manifolds with boundary (and interiors of such manifolds, it's the same thing), we have a paper with Campos, Lambrechts, and Willwacher, where we also give a real model (several, in fact). If $\dim M \ge 4$ then this model is fairly explicit, otherwise it's complicated.


Besides all the models we give are equipped with a symmetric group action that models the natural symmetric group action on $\operatorname{Conf}_k(M)$, so if you are interested in unordered configuration spaces then you can compute their cohomology by considering invariants.
A: I would be extremely surprised if there was anything other than the Cohen-Taylor spectral sequence that you can do in this generality.
As you know, the first nontrivial page of Cohen-Taylor spectral sequence depends only on the ring $H^\bullet(M)$. I think it's written up somewhere that the higher order differentials are defined by Massey products on $M$. In particular the result you refer to in a comment that $H^\bullet(F(M,n))$ (or its associated graded) can be computed explicitly from $H^\bullet(M)$ extends to arbitrary formal manifolds $M$, not just smooth projective varieties. And if you give yourself a minimal model of $M$ you should be able to compute $H^\bullet(F(M,n))$ for all $n$ as well (but not a minimal model of $F(M,n)$ -- see the paper of Longoni and Salvatore).
