Let be a simply connected closed manifold and consider the (ordered) configuration space of points in . In this paper we construct a commutative differential graded algebra which is a potential candidate for a model of the rational homotopy type of . We prove that our model it is at least a –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.
"A remarkable DGmodule model for configuration spaces." Algebr. Geom. Topol. 8 (2) 1191 - 1222, 2008. https://doi.org/10.2140/agt.2008.8.1191