论文标题
关于Artin组的抛物线亚组
On parabolic subgroups of Artin groups
论文作者
论文摘要
给定一个Artin Group $A_γ$，研究$A_γ$的一种常见策略是将其定义图的直径较小的抛物线子亚组减少，即表明$A_γ$具有特定的特定属性，并且仅当所有“小”抛物面子组为$A_γ$。由于“小”抛物线亚组是$a_γ$的拼图，因此需要研究其行为，尤其是它们的交叉点。我们在这里解决的猜想说，$A_γ$的抛物线子组类别在交叉点下关闭。在完全抛物线中的抛物线亚组相交的假设是，我们表明完整的抛物线亚组与任意抛物线亚组的交点是抛物线。此外，我们使用低音 - 塞雷理论和deligne复合物的概括将$a_γ$的完整抛物线亚组的交点行为与$a_γ$的自动连续性联系起来。
Given an Artin group $A_Γ$, a common strategy in the study of $A_Γ$ is the reduction to parabolic subgroups whose defining graphs have small diameter, i.e. showing that $A_Γ$ has a specific property if and only if all "small" parabolic subgroups of $A_Γ$ have this property. Since "small" parabolic subgroups are the puzzle pieces of $A_Γ$ one needs to study their behavior, in particular their intersections. The conjecture we address here says that the class of parabolic subgroups of $A_Γ$ is closed under intersection. Under the assumption that intersections of parabolic subgroups in complete Artin groups are parabolic, we show that the intersection of a complete parabolic subgroup with an arbitrary parabolic subgroup is parabolic. Further, we connect the intersection behavior of complete parabolic subgroups of $A_Γ$ to fixed point properties and to automatic continuity of $A_Γ$ using Bass-Serre theory and a generalization of the Deligne complex.
