论文标题
相对双曲的度量束和大炮 - 瑟斯顿地图
Relatively hyperbolic metric bundles and Cannon-Thurston map
论文作者
论文摘要
鉴于$ b $上的度量（图）捆绑$ x $，其中所有纤维都是强烈的双曲线和非元素，我们表明，在某些条件下，相对于holosphere样空间的最大圆锥体的集合，$ x $具有强烈的双曲线。此外，鉴于嵌入$ i：a \ to b $的粗lipschitz Qi，我们证明了回调$ y $非常相对夸张，并且地图$ y \ x $ to x $允许Cannon-Thurston（CT）地图。作为一种应用，我们证明了该结果的组理论类似物，用于组的相对双曲扩展。
Given a metric (graph) bundle $X$ over $B$ where all the fibres are strongly relatively hyperbolic and nonelementary we show that, under certain conditions, $X$ is strongly hyperbolic relative to a collection of maximal cone-subbundles of horosphere-like spaces. Further, given a coarsely Lipschitz qi embedding $i: A\to B$, we show that the pullback $Y$ is strongly relatively hyperbolic and the map $Y\to X$ admits a Cannon-Thurston (CT) map. As an application, we prove a group-theoretic analogue of this result for a relatively hyperbolic extension of groups.
