In this paper we provide descriptions of the Whitehead groups withcoefficients in a ring of the Hilbert modular group and its reduced version, aswell as for the topological K-theory of $C^*$-algebras, after tensoring with$\mathbb{Q}$, by computing the source of the assembly maps in the Farrell-Jonesand the Baum-Connes conjecture respectively. We also construct a model for theclassifying space of the Hilbert modular group for the family of virtuallycyclic subgroups.
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机译：在本文中，我们描述了在Hilbert模块化组及其简化版的一个环中具有系数的Whitehead组的描述，以及在用$ \ mathbb {Q}张量后的$ C ^ * $-代数的拓扑K-理论。 $，分别通过计算Farrell-Jones和Baum-Connes猜想中的装配图的来源。我们还为虚拟循环子群族构建了一个希尔伯特模块化群空间分类模型。
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