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We produce new cohomology for non-uniform arithmetic lattices using a technique of Millson–Raghunathan. From this, we obtain new characteristic classes of manifold bundles with fiber a closed -dimensional manifold with indefinite intersection form of signature . These classes are defined on finite covers of Diff and are shown to be nontrivial for . In this case, the classes produced live in degree 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.
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Bena Tshishiku, Geometric cycles and characteristic classes of manifold bundles. Comment. Math. Helv. 96 (2021), no. 1, pp. 1–45DOI 10.4171/CMH/505