论文标题
戴维斯·穆斯蒙综合体的概括为染料组
A generalization of the Davis-Moussong complex for Dyer groups
论文作者
论文摘要
Coxeter组和右角ARTIN组的共同特征是他们对单词问题的解决方案。马修·戴尔（Matthew Dyer）介绍了一类小组，我们将其称为Dyer群体，分享了此功能。该类包括但不限于Coxeter组，右角Artin组和循环组的图形产品。我们通过给出标准介绍并表明它们是Coxeter组的有限指数亚组来介绍染料组。然后，我们引入了一个分段欧几里得细胞复合物$σ$，该$σ$概括了戴维斯·穆斯蒙综合体和萨尔维蒂综合体。 $σ$的构建使用简单的类别，没有循环和组的复合物。我们通过证明细胞复杂$σ$是CAT（0）来得出结论。
A common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. Matthew Dyer introduced a class of groups, which we call Dyer groups, sharing this feature. This class includes, but is not limited to, Coxeter groups, right-angled Artin groups, and graph products of cyclic groups. We introduce Dyer groups by giving their standard presentation and show that they are finite index subgroups of Coxeter groups. We then introduce a piecewise Euclidean cell complex $Σ$ which generalizes the Davis-Moussong complex and the Salvetti complex. The construction of $Σ$ uses simple categories without loops and complexes of groups. We conclude by proving that the cell complex $Σ$ is CAT(0).
