Differential forms and the Wodzicki residue

Details Differential forms and the Wodzicki residue Differential forms and the Wodzicki residue

2002-11-22

arxiv.org/abs/math/0211361v2

Mathematics

Differential Geometry

20 pages

Scientific paper

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 $C^\infty(M)\times C^\infty(M)$. This differential form $\Omega_{n,S}$ is given in terms of the Wodzicki 1-density $\wres([S,f][S,h])$. In the particular case of an even dimensional, compact, conformal manifold without boundary, we study this differential form for the case $(B,S)=(\cH,F)$, 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.

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