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We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.
We prove that the rational homotopy type of the configuration space of two points in a
-connected closed manifold depends only on the rational homotopy type of that manifold
and we give a model in the sense of Sullivan of that configuration space. We also study
the formality of configuration spaces.
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