Abstract
It is shown that the existence of a global gravitational anomaly in string theory on a ten-dimensional spacetime M under a coordinate transformation pi is related to an invariant of the smooth structure of an 11-manifold associated to M and pi . The cancellation of global gravitational anomalies in ten-dimensional flat space follows from the fact that the 11-sphere admits exactly 992 distinct smooth structures. The possibility of an anomaly occurring on a general spacetime can be discussed in terms of smoothing theory.