# 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

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