论文标题
有限生成的组的离散表示为$ {\ rm psl}（2，\ mathbb {r}）$
Discrete representations of finitely generated groups into ${\rm PSL}(2,\mathbb{R})$
论文作者
论文摘要
我们证明了与Agol和Liu相似的紫红色群体的分解定理。作为一个应用程序，我们构建了makanin-razborov图，该图参数从任意但固定的有限生成的组$ g $到$ {\ rm psl}（2，\ mathbb {r}）$的所有离散表示的收集。我们定义了一个称为$ {\ rm psl}（2，\ mathbb {r}）$的新组组 - 离散限制组，然后使用分解定理获取有关此类组的有用信息。
We prove a factorization theorem for Fuchsian groups similar to those proved by Agol and Liu for 3-manifold groups. As an application, we build Makanin-Razborov diagrams, which parametrize the collection of all discrete representations from an arbitrary but fixed finitely generated group $G$ to ${\rm PSL}(2, \mathbb{R})$. We define a new class of groups called ${\rm PSL}(2, \mathbb{R})$-discrete limit groups and then use the factorization theorem to obtain useful information about this class of groups.
