非球面流形重言类的一个消灭定理
A vanishing theorem for tautological classes of aspherical manifolds
摘要：
重言类，或广义Miller-Morita-Mumford类，是光滑纤维丛的基本特征类，最近被用来描述几种流形的类同态群的分类空间的有理上同调。我们合理重言类只依赖于基本的拓扑块丛，并利用这一点来证明消失的重言类的许多丛纤维的非球面流形。
英文摘要：
Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational cohomology of classifying spaces of diffeomorphism groups for several types of manifolds. We show that rationally tautological classes depend only on the underlying topological block bundle, and use this to prove the vanishing of tautological classes for many bundles with fibre an aspherical manifold.
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