2002/11/15 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/0211240
13 pages, LaTeX
arxiv created 2003/02/27 · arxiv updated 2009/11/30
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 \Wres(f0[F,f][F,h]) = ∫M f0Ω6(f,h) for (\cH,F) the Fredholm module associated by A. Connes \citeCon1 to the manifold M, and \Wres the Wodzicki residue.