论文标题
右角建筑物及其通用团体的城市产品
City products of right-angled buildings and their universal groups
论文作者
论文摘要
我们介绍了右角建筑物的城市产品的概念，该建筑物由较小建筑物产生新的右角建筑物。 更确切地说，如果$ m $是右角$ n $和$δ_1，\ dots，δ_n$的右角coxeter图，则是右角建筑物，那么我们构建了一个新的右角建筑物$δ：= \ m athrm {cityproduct} _m（Δ_1，\ dex_1，\ dots，\ dots，Δ____________________n）$。我们可以从$δ$的残基中恢复$Δ_1，\ dots，δ_n$，但我们还可以从$δ$中构建$ m $ type $ m $的骨骼建筑，从而捕获$Δ$的大规模几何形状。 然后，我们继续研究右角建筑物的城市产品的通用小组，我们表明，可以用建筑物的通用组来表达$δ__1，\ dots，δ_n$的通用组和$ m $ $ m $的结构。作为应用程序，我们展示了许多对（拓扑）同构普遍组的相同类型的不同建筑物对的示例，从而大大概括了LaraBeßmann的最新示例。
We introduce the notion of city products of right-angled buildings that produces a new right-angled building out of smaller ones. More precisely, if $M$ is a right-angled Coxeter diagram of rank $n$ and $Δ_1,\dots,Δ_n$ are right-angled buildings, then we construct a new right-angled building $Δ:= \mathrm{cityproduct}_M(Δ_1,\dots,Δ_n)$. We can recover the buildings $Δ_1,\dots,Δ_n$ as residues of $Δ$, but we can also construct a skeletal building of type $M$ from $Δ$ that captures the large-scale geometry of $Δ$. We then proceed to study universal groups for city products of right-angled buildings, and we show that the universal group of $Δ$ can be expressed in terms of the universal groups for the buildings $Δ_1,\dots,Δ_n$ and the structure of $M$. As an application, we show the existence of many examples of pairs of different buildings of the same type that admit (topologically) isomorphic universal groups, thereby vastly generalizing a recent example by Lara Beßmann.
