Parallel forms, co-K\"ahler Manifolds and their Models

We show how certain topological properties of co-K"ahler manifolds derive from those of the K"ahler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-K"ahler manifold reduces the computation of cohomology from the de Rham complex to certain amenable sub-cdga’s defined by geometrically natural operators derived from the co-K"ahler structure. This provides a simpler proof of the formality of the foliation minimal model in this context.