Homotopy graph-complex for configuration and knot spaces
  In the paper we prove that the primitive part of the Sinha homology spectral sequence E^2-term for the space of long knots is rationally isomorphic to the homotopy E^2-term.   We also define natural graph-complexes computing the rational homotopy of configuration and of knot spaces. 
Pascal Lambrechts, Victor Tourtchine