JournalscmhVol. 96, No. 1pp. 1–45

Geometric cycles and characteristic classes of manifold bundles

  • Bena Tshishiku

    Harvard University, Cambridge, USA
Geometric cycles and characteristic classes of manifold bundles cover
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Abstract

We produce new cohomology for non-uniform arithmetic lattices Γ<SO(p,q)\Gamma < \mathrm {SO}(p,q) using a technique of Millson–Raghunathan. From this, we obtain new characteristic classes of manifold bundles with fiber a closed 4k4k-dimensional manifold MM with indefinite intersection form of signature (p,q)(p,q). These classes are defined on finite covers of BB Diff (M)(M) and are shown to be nontrivial for M=#g(S2k×S2k)M=\#_g(S^{2k}\times S^{2k}). In this case, the classes produced live in degree gg 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.

Cite this article

Bena Tshishiku, Geometric cycles and characteristic classes of manifold bundles. Comment. Math. Helv. 96 (2021), no. 1, pp. 1–45

DOI 10.4171/CMH/505