A remarkable DGmodule model for configuration spaces

Abstract

Let $M$ be a simply connected closed manifold and consider the (ordered) configuration space $F\left(M,k\right)$ of $k$ points in $M$. In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the rational homotopy type of $F\left(M,k\right)$. We prove that our model it is at least a ${\Sigma }_k$–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.