Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Sylvie Paycha (Uni Potsdam)
Inspired by Gilkey's invariance theory, Connes' deformation to the normal cone and Getzler's rescaling method, we single out a class of geometric operators among pseudodifferential operators acting on sections of a class of natural vector bundles, to which we attach a rescaling degree.
This degree is then used to express regularised traces of geometric operators in terms of a rescaled limit of Wodzicki residues. When applied to complex powers of the square of a Dirac operator, this amounts to expressing the index of a Dirac operator in terms of a local residue involving the Getzler rescaled limit of its square.