The Koszul or bar duality between operads can be defined in the categories of chain complexes or spectra.

An important case is that of the E_n operad, that is self-dual up to a shift. In this case using configuration spaces models one obtains a form of Poincare duality. Another interesting case is the duality between open and closed moduli space of genus zero curves, where the bar construction gives an explicit cellular decomposition of the Deligne-Mumford compactification.

This is partially joint work with Ching and Rossi.