论文标题
相对双曲线的边界的局部连接
Local connectedness of boundaries for relatively hyperbolic groups
论文作者
论文摘要
令$（γ，\ mathbb {p}）$为相对双曲的组对，相对结束。然后，$（γ，\ mathbb {p}）$的Bowditch边界是本地连接的。 Bowditch先前在其他假设中确立了这一结论，即所有外围亚组有限地呈现，一个或两个结束，并且不包含无限的扭转亚组。我们消除了这些限制；我们对$γ$的基数没有限制，也不限制\ Mathbb {p} $的外围子组$ p \。
Let $(Γ,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(Γ,\mathbb{P})$ is locally connected. Bowditch previously established this conclusion under the additional assumption that all peripheral subgroups are finitely presented, either one or two ended, and contain no infinite torsion subgroups. We remove these restrictions; we make no restriction on the cardinality of $Γ$ and no restriction on the peripheral subgroups $P \in \mathbb{P}$.
