Multiplicative models for configuration spaces of algebraic varieties

We construct an even simpler and smaller model, Jn(H). We then define another new dg-algebra, En(H∘), and use Jn(H) to prove that En(H∘) is a model of the space of n-configurations of the non-compact punctured manifold X∘, when X is 1-connected. Following an idea of Drinfel'd (Leningrad Math. J. 2 (1991) 829), we put a simplicial bigraded differential algebra structure on {En(H∘)}n⩾0.