Differential forms canonically associated to even-dimensional compact conformal manifolds

الأصل · EN

On a 6-dimensional, conformal, oriented, compact manifold M without boundary, we compute a whole family of differential forms Ω₆(f,h) of order 6, with f,h ∈ C∞(M). Each of these forms will be symmetric on f, and h, conformally invariant, and such that ∫ₘ f₀ Ω₆(f₁,f₂) defines a Hochschild 2-cocycle over the algebra C∞(M). In the particular 6-dimensional conformally flat case, we compute the unique one satisfying (f₀[F,f][F,h]) = ∫ₘ f₀Ω₆(f,h) for (,F) the Fredholm module associated by A. Connes Con1 to the manifold M, and the Wodzicki residue.