Differential forms and the Wodzicki residue

الأصل · EN

For a pseudodifferential operator S of order 0 acting on sections of a vector bundle B on a compact manifold M without boundary, we associate a differential form of order dimension of M acting on C∞(M)× C∞(M). This differential form Ωₙ,ₛ is given in terms of the Wodzicki 1-density ([S,f][S,h]). In the particular case of an even dimensional, compact, conformal manifold without boundary, we study this differential form for the case (B,S)=(,F), that is, the Fredholm module associated by A. Connes to the manifold M. We give its explicit expression in the flat case and then we address the general case.