We produce new cohomology for non-uniform arithmetic lattices $\Gamma < \mathrm {SO}(p,q)$ using a technique of Millson–Raghunathan. From this, we obtain new characteristic classes of manifold bundles with fiber a closed $4k$-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 $M=\#_g(S^{2k}\times S^{2k})$. 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.

中文翻译：

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歧管束的几何循环和特征类别

我们使用Millson–Raghunathan技术对非均匀算术格$ \ Gamma <\ mathrm {SO}（p，q）$产生了新的同调。由此，我们获得具有纤维的，具有封闭的$ 4k $维歧管$ M $且具有签名$（p，q）$的不定相交形式的歧管束的新特征类。这些类在$ B $ Diff $（M）$的有限覆盖范围上定义，并且对于$ M = \ #_ g（S ^ {2k} \ times S ^ {2k}）$而言，显示为非平凡的。在这种情况下，所产生的类的生存度为$ g $，并且与稳定（即MMM）类所生成的代数无关。我们还提供了将纤维束捆绑在K3表面上的应用程序。