Differential Forms Canonically Associated to Even-Dimensional Compact Conformal Manifolds

On a 6-dimensional, conformal, oriented and compact manifold M without boundary we compute a whole family of differential forms Ω₆(f, h) of order 6 with f, h ξ C∞(M). Each of these forms will be symmetric on f and h, conformally invariant, and such that ∫ _Mf₀Ω₆(f₁, f₂) defines a Hochschild 2-cocycle over the algebra C∞ (M). In the particular 6-dimensional conformally flat case, we compute a unique form satisfying Wres(f₀[F,f][F, h])=∫_Mf₀Ω₆(f, h) for the Fredholm module (H, F) associated by A. Connes [6] to the manifold M, and the Wodzicki residue Wres.