2008/09/14 by Tadler, Thomas, longoni, Riccardo
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.0809.2380
We introduce the notion of homotopy inner products for any cyclic quadratic Koszul operad \mathcal O, generalizing the construction already known for the associative operad. This is done by defining a colored operad \widehat\mathcal O, which describes modules over \mathcal O with invariant inner products. We show that \widehat\mathcal O satisfies Koszulness and identify algebras over a resolution of \widehat\mathcal O in terms of derivations and module maps. As an application we construct a homotopy inner product over the commutative operad on the cochains of any Poincaré duality space.