论文标题
垂直空间的收缩边界
Contracting Boundary of a Cusped Space
论文作者
论文摘要
令$ g $为有限生成的组。 Cashen和Mackay证明，如果$ g $的合同边界与旅行准地球学的拓扑结合在一起，那么$ G $是一个双曲线组。令$ \ Mathcal {H} $为有限生成的无限索引子组的有限集合。令$ g^h $为通过将组合horoballs连接到$ \ Mathcal {h} $的每个左侧comets获得的cusped空间。在本文中，我们证明，如果组合horoballs正在签约并且$ g^h $具有紧凑的收缩边界，那么$ g $是相对于$ \ Mathcal {h} $的双曲线。
Let $G$ be a finitely generated group. Cashen and Mackay proved that if the contracting boundary of $G$ with the topology of fellow travelling quasi-geodesics is compact then $G$ is a hyperbolic group. Let $\mathcal{H}$ be a finite collection of finitely generated infinite index subgroups of $G$. Let $G^h$ be the cusped space obtained by attaching combinatorial horoballs to each left cosets of elements of $\mathcal {H}$. In this article, we prove that if the combinatorial horoballs are contracting and $G^h$ has compact contracting boundary then $G$ is hyperbolic relative to $\mathcal{H}$.
