A remarkable DG-module model for configuration spaces

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Let M be a simply-connected closed manifold and consider the (ordered) configuration space of k points in M, F(M,k). In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the rational homotopy type of F(M,k). We prove that our model it is at least a Sigmaₖ-equivariant differential graded model. We also study Lefschetz duality at the level of cochains and describe equivariant models of the complement of a union of polyhedra in a closed manifold.