Differential forms and the Wodzicki residue

2002/11/22 by William J. Ugalde, Ugalde, William J.
Mathematics · #46L87 #53A30 #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #math.DG #math.OA #msc:46L87 #msc:53A30

paper · pdf · doi:10.48550/arxiv.math/0211361

20 pages

arxiv created 2003/02/27 · arxiv updated 2009/11/30

Abstract

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 Ω_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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