# Geometric cycles and characteristic classes of manifold bundles

with appendix by M. Krannich

### Comment. Math. Helv. 96 (2021) 1, 1-45.

We produce new cohomology for non-uniform lattices in SO(p,q) using a technique of Millson-Raghunathan. From this, we obtain new characteristic classes for manifold bundles with fiber a closed 4k-dimensional manifold M with indefinite intersection form of signature (p,q). These characteristic classes are defined on finite covers of BDiff(M) and are shown to be nontrivial for connected sums of S^{2k} x S^{2k}. In this cases the classes produced live in degree g and are indepdendent from the algebra generated by the stable (i.e. MMM) classes. We also give an application to bundles with fiber a K3 surface.