Filtern
Volltext vorhanden
- ja (1)
Erscheinungsjahr
- 2011 (1)
Dokumenttyp
- Postprint (1) (entfernen)
Sprache
- Englisch (1) (entfernen)
Gehört zur Bibliographie
- ja (1) (entfernen)
Schlagworte
- index (1) (entfernen)
Institut
- Mathematisch-Naturwissenschaftliche Fakultät (1) (entfernen)
We show that the residue density of the logarithm of a generalized 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 formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a
twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell–Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.