On global anomalies in type IIB string theory

We study global gravitational anomalies in type IIB string theory with nontrivial middle cohomology. This requires the study of the action of diffeomorphisms on this group. Several results and constructions, including some recent vanishing results via elliptic genera, make it possible to consider this problem. Along the way, we describe in detail the intersection pairing and the action of diffeomorphisms, and highlight the appearance of various structures, including the Rochlin invariant and its variants on the mapping torus.