Poincaré duality and commutative differential graded algebras

Abstract

We prove that every Commutative differential graded algebra whose cohomology is a simply-connected Poincare duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincare duality in the same dimension. This has applications in rational homotopy, giving Poincare duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.