论文标题
相对双曲组的组合定理和分裂的有限相对高度
A combination theorem for relatively hyperbolic groups and finite relative height of splitting
论文作者
论文摘要
在本文中，我们证明了相对双曲基团的相对酰基的组合定理（定理1.1）。在这里，我们正在扩展[TOM21]的技术和构建基本图基群的Bowditch边界。假设g（y）是相对双曲线组的图，例如边缘组是相邻顶点组中相对较准分的。另外，假设G（Y）的基本组相对双曲。然后，我们表明g（y）的边缘组具有有限的相对高度（定义1.5），并且仅当它们是相对较高的coSi-convex（定理1.6）时。在最后一节中，我们提供了一个申请。
In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of graph of groups. Suppose G(Y) is a graph of relatively hyperbolic groups such that edge groups are relatively quasi-convex in adjacent vertex groups. Also, assume that the fundamental group of G(Y) is relatively hyperbolic. Then we show that the edge groups of G(Y) have finite relative height (Definition 1.5) if and only if they are relatively quasi-convex (Theorem 1.6). In the last section, we give an application.
