论文标题
粗立方刚度
Coarse cubical rigidity
论文作者
论文摘要
我们表明，对于许多右角Artin和Coxeter群体，所有共同体群都看起来相同：它们在该组上诱导相同的粗糙中位结构。这些是该特性的非纤维化群体的第一个例子。 对于所有有限基团的图形产品，对于没有等级$ \ geq 3 $的不可还原仿射抛物线亚组的Coxeter组，我们表明，所有自动形态都保留了戴维斯建筑群和Niblo-reebreves Cubulation诱导的粗糙中位结构。结果，这些群体的自身形态具有良好的固定亚组，并满足了尼尔森的实现。
We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this property. For all graph products of finite groups and for Coxeter groups with no irreducible affine parabolic subgroups of rank $\geq 3$, we show that all automorphism preserve the coarse median structure induced, respectively, by the Davis complex and the Niblo-Reeves cubulation. As a consequence, automorphisms of these groups have nice fixed subgroups and satisfy Nielsen realisation.
