发表机构
Luis Paris, Universit\'e Bourgogne Europe, CNRS, IMB, UMR 5584, 21000 Dijon, France.
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究围绕虚拟阿廷群展开，通过关联元素复形构造对应的立方体复形，证明其连通、单连通、局部正则等性质，还得出该复形为CAT(0)的充要条件是对应元素复形为旗复形。
AI 中文摘要
设$Γ$为一个Coxeter图，$S$为其顶点集。$Γ$上的元素复形是$S$上的抽象单纯复形$\mathcal D$，它包含每一对满足$s \neq t$和$m_{s,t} \neq \infty$的$\{s, t\}$。对于每个元素复形$\mathcal D$，我们将一个立方体复形$Ξ_\mathcal D$与之关联，虚拟阿廷群$\rm VA [Γ]$在该立方体复形上作用。我们证明$Ξ_\mathcal D$连通、单连通且局部正则；$\rm VA[Γ]$在$Ξ_\mathcal D$上的作用是正则、余紧且通过等距变换实现的；胞腔的稳定子群是抛物子群。最后，我们证明$\XiÆ’_\mathcal D$为CAT(0)当且仅当$\mathcal D$是旗复形。
英文摘要
Let $Γ$ be a Coxeter graph, and let $S$ be its vertex set. An elemental complex over $Γ$ is an abstract simplicial complex $\mathcal D$ on $S$ that contains every pair $\{s, t\}$ with $s \neq t$ and $m_{s,t} \neq \infty$. To each elemental complex $\mathcal D$, we associate a cube complex $Ξ_{\mathcal D}$ on which the virtual Artin group ${\rm VA} [Γ]$ acts. We prove that $Ξ_{\mathcal D}$ is connected, simply connected, and locally regular; that the action of ${\rm VA}[Γ]$ on $Ξ_{\mathcal D}$ is regular, cocompact, and by isometries; and that the stabilizers of cells are parabolic subgroups. We finally prove that $Ξ_{\mathcal D}$ is CAT(0) if and only if ${\mathcal D}$ is a flag complex.
