The action dimension of a discrete group $G$ is the minimum dimension of a contractible manifold that admits a proper $G$‐action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including (1) Artin groups, (2) graph products of groups and (3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.

中文翻译：

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组的一些简单复合体的动作维

离散组的动作维度 $G$ 是可收缩歧管的最小尺寸 $G$-行动。我们为几类示例计算了一组简单组合的直接极限的作用维，这些示例包括（1）Artin组，（2）组的图形乘积和（3）仿射超平面排列的非球面补码的基本组。