Homotopy graph-complex for configuration and knot spaces

Abstract

We prove that the primitive part of the Sinha homology spectral sequence E 2 E^2 -term for the space of long knots is rationally isomorphic to the homotopy E 2 \mathcal {E}^2 -term. We also define natural graph-complexes computing the rational homotopy of configuration and of knot spaces.