The logarithmic residue density of a generalised Laplacian

@inproceedings{Mickelsson2010TheLR,
  title={The logarithmic residue density of a generalised Laplacian},
  author={Jouko Mickelsson and Sylvie Jane Ann Paycha},
  year={2010}
}
We show that the residue density of the logarithm of a generalised Laplacian on a closed manifold defines an invariant polynomial valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulae provide a pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in dimension $4$ and for a twisted Dirac operator on a flat space of any dimension. These correspond to… CONTINUE READING