论文标题
群落条件
Link conditions for cubulation
论文作者
论文摘要
我们在多边形复合物的链接上提供条件，足以确保在此类复合物上正确地作用的组正确起作用。我们在多边形复合物的链接上提供了更强的条件，这些条件足以确保在此类复合物上正确作用的小组在猫（0）Cube Complex上正确地作用于此类复合物。如果该组是双曲线，那么此操作也是共同的，因此，通过Agol定理，该组几乎是特殊的（从Haglund的意义上讲）；特别是在Z上是线性的。我们考虑了这项工作的某些应用。首先，我们将[KV10]和[CKV12]分类的群体简单地在CAT（0）三角形复合物上起作用，并以最小的广义四边形为它们，证明了这些群体实际上很特别。我们通过考虑广义三角组，特别是[CCKW20]考虑的子集进一步应用该定理。
We provide a condition on the links of polygonal complexes that is sufficient to ensure groups acting properly discontinuously and cocompactly on such complexes contain a virtually free codimension-1 subgroup. We provide stronger conditions on the links of polygonal complexes, which are sufficient to ensure groups acting properly discontinuously and cocompactly on such complexes act properly discontinuously on a CAT(0) cube complex. If the group is hyperbolic then this action is also cocompact, hence by Agol's Theorem the group is virtually special (in the sense of Haglund-Wise); in particular it is linear over Z. We consider some applications of this work. Firstly, we consider the groups classified by [KV10] and [CKV12], which act simply transitively on CAT(0) triangular complexes with the minimal generalized quadrangle as their links, proving that these groups are virtually special. We further apply this theorem by considering generalized triangle groups, in particular a subset of those considered by [CCKW20].
