On the Homology of Spaces of Long Knots

This paper is a more detailed version of [38], where the first term of the Vassiliev spectral sequence (computing the homology of the space of long knots in Rd, d ≥ 3) was described in terms of the Hochschild homology of the Poisson algebras operad for d odd, and of the Gerstenhaber algebras operad for d even. In particular, the bialgebra of chord diagrams arises as some subspace of this homology. The homology in question is the space of characteristic classes for Hochschild cohomology of Poisson (resp. Gerstenhaber) algebras considered as associative algebras. The paper begins with necessary preliminaries on operads.