Geometric cycles and characteristic classes of manifold bundles. (arXiv:1711.03139v1 [math.GT])

We introduce new characteristic classes of manifold bundles with fiber a closed $4k$-dimensional manifold $M$ with indefinite intersection form of signature $(p,q)$. These characteristic classes originate in the homology of arithmetic subgroups of SO$(p,q)$. We prove that our characteristic classes are nontrivial for $M = \#_g(S^{2k}\times S^{2k})$. In this case, the classes we produce live in degree $g$ and are independent from the algebra generated by the stable (i.e. MMM) classes. 查看全文>>