离散群空间分类的拓扑K理论的有理计算
Rational Computations of the Topological K-Theory of Classifying Spaces of Discrete Groups
摘要：
我们合理地计算了离散群的分类空间BG的拓扑（复）K-理论，条件是G的分类空间对于适当的G-作用有一个上紧的G-CW-模型。例如，字双曲群和连通李群的余紧离散子群满足这个假设。答案是根据G的群上同调和素数幂阶有限循环子群的中心化子给出的。我们还分析了乘法结构。
英文摘要：
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and cocompact discrete subgroups of connected Lie groups satisfy this assumption. The answer is given in terms of the group cohomology of G and of the centralizers of finite cyclic subgroups of prime power order. We also analyze the multiplicative structure.
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