Geometric cycles and characteristic classes of manifold bundles

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