论文标题
投影复合物的双曲线商
Hyperbolic quotients of projection complexes
论文作者
论文摘要
本文是我们以前与玛格丽特（Margalit）的工作的延续，在那里我们研究了针对投影复合物的小组行动。在该论文中，我们证明了足够的条件，因此顶点稳定剂子组的正常闭合是这些亚组某些偶联物的免费产物。在本文中，我们研究了这个正常亚组的投影复合物的商，又研究商组对投影络合物商的作用。我们表明，在某些条件下，商复合物为$δ$ hyperbolic。此外，在某些情况下，我们表明，如果投影复合物上的原始动作是非元素的WPD动作，那么商组对投影综合体商的作用也是如此。这意味着商组是酰基柔毛的。
This paper is a continuation of our previous work with Margalit where we studied group actions on projection complexes. In that paper, we demonstrated sufficient conditions so that the normal closure of a family of subgroups of vertex stabilizers is a free product of certain conjugates of these subgroups. In this paper, we study both the quotient of the projection complex by this normal subgroup and the action of the quotient group on the quotient of the projection complex. We show that under certain conditions that the quotient complex is $δ$-hyperbolic. Additionally, under certain circumstances, we show that if the original action on the projection complex was a non-elementary WPD action, then so is the action of the quotient group on the quotient of the projection complex. This implies that the quotient group is acylindrically hyperbolic.
