#### Volume 8, issue 2 (2008)

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A remarkable DGmodule model for configuration spaces

### Pascal Lambrechts and Don Stanley

Algebraic & Geometric Topology 8 (2008) 1191–1222
##### 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.

##### Keywords
Poincaré duality, Lefschetz duality, Sullivan model, configuration spaces
##### Mathematical Subject Classification 2000
Primary: 55P62, 55R80