论文标题
从纤维中传播准烟气
Propagating quasiconvexity from fibers
论文作者
论文摘要
令$ 1 \到k \ longrightArrow g \stackrelπ\ longrightArrow q $是双曲线组的精确序列。令$ q_1 <q $为Quasiconvex子组，让$ g_1 =π^{ - 1}（q_1）$。在相对温和的条件下（例如，如果$ k $是一个封闭的表面组或一个免费组，$ q $是凸Cocompact），我们表明，$ g_1 $的无限索引Quasiconvex亚组为$ g $。相关结果已被证明是指标束，组的开发复合物和组图。
Let $1 \to K \longrightarrow G \stackrelπ\longrightarrow Q$ be an exact sequence of hyperbolic groups. Let $Q_1 < Q$ be a quasiconvex subgroup and let $G_1=π^{-1}(Q_1)$. Under relatively mild conditions (e.g. if $K$ is a closed surface group or a free group and $Q$ is convex cocompact), we show that infinite index quasiconvex subgroups of $G_1$ are quasiconvex in $G$. Related results are proven for metric bundles, developable complexes of groups, and graphs of groups.
