Gravitational anomaly cancellation and modular invariance

Abstract

In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For(4k +2)-dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaumé and Witten in dimensions 2, 6 and 10 [1] as special cases. In dimension 4k +1, we derive anomaly cancellation formulas for index gerbes. In dimension 4k+3, we obtain certain results about eta invariants, which are interesting in spectral geometry.