论文标题
晶体学HELLY组
Crystallographic Helly Groups
论文作者
论文摘要
我们证明，Helly图的渐近锥是次数超凸。我们用它来表明，实际上nilpotent helly群体实际上是Abelian，并且通过其点组来表征几乎Abelian Helly组。实际上，我们为更粗糙的注入空间和组的更一般的类别做到这一点。我们将其应用于证明，$ 3 $ - $ 3 $ - $ 3 $ -OCOXETER GROUP并不是Helly（甚至是粗略的注入），从而获得了一个没有Helly的收缩期组的第一个例子，回答了Chalopin，Chalopin，Chepoi，Genevois，Genevois，Hirai和Osajda的问题。
We prove that asymptotic cones of Helly graphs are countably hyperconvex. We use this to show that virtually nilpotent Helly groups are virtually abelian and to characterize virtually abelian Helly groups via their point groups. In fact, we do this for the more general class of coarsely injective spaces and groups. We apply this to prove that the $3$-$3$-$3$-Coxeter group is not Helly (nor even coarsely injective), thus obtaining the first example of a systolic group that is not Helly, answering a question of Chalopin, Chepoi, Genevois, Hirai, and Osajda.
