余紧立方晶体群
Cocompactly cubulated crystallographic groups
摘要：
我们证明了CAT（0）立方体复形的单纯边界与$\integers^n$的超八面体三角剖分同构，从而给出了一类$G$ -余紧立方体复形的单纯边界只依赖于$G$的群.我们也用这个结果来说明，在$n$维上的共配位晶体群正是那些\emph{hyperoctahedral}。我们应用这个结果来回答Wise关于协紧群的一个问题，它是关于自由阿尔贝群的.
英文摘要：
We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually $\integers^n$ group is isomorphic to the hyperoctahedral triangulation of $S^{n-1}$, providing a class of groups $G$ for which the simplicial boundary of a $G$-cocompact cube complex depends only on $G$. We also use this result to show that the cocompactly cubulated crystallographic groups in dimension $n$ are precisely those that are \emph{hyperoctahedral}. We apply this result to answer a question of Wise on cocompactly cubulating virtually free abelian groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
