On the topological interpretation of gravitational anomalies

Abstract

We consider the mixed gravitational Yang–Mills anomaly as the coupling between the K-theory and K-homology of a C ∗ -algebra crossed product. The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras.