GEOMETRIC BEHAVIOUR OF KLEINIAN GROUPS ON BOUNDARIES FOR DEFORMATION SPACES
GEOMETRIC BEHAVIOUR OF KLEINIAN GROUPS ON BOUNDARIES FOR DEFORMATION SPACES
复制标题
变形空间边界上克莱尼群的几何行为
DOI：
10.1093/qmath/43.1.97
复制
发表时间：
1992
影响因子：
0.7
通讯作者：
Ken'ichi Ohshika
中科院分区：
文献类型：
--
作者：
Ken'ichi Ohshika
让我们成为Kleinian小组。设{F，}是同构的Kleinian群序列{<£，：F - > F,-}。假设#收敛于同构ip: F - >g作为F到PSL2C的表示。设H为{F，} c PSL2C的几何极限。在这种情况下，我们想知道G和H重合的时候，以及G和H不重合时H族是什么。本文在假设F是Thurston意义上的几何驯服群的前提下考虑这些问题。首先在§2中，我们给出代数极限与几何极限重合的一个充分条件。声明如下。
LET T be a Kleinian group. Let {F,} be a sequence of Kleinian groups with isomorphisms {<£,: F—> F,-}. Suppose that#, converges to an isomorphism ip: F—> G as representations of F into PSL2C. Let H be the geometric limit of {F,} c PSL2C. In this situation, we want to know when G and H coincide, and what group H can be when G and H do not coincide.In this paper we consider these questions under the assumption that F is a geometrically tame group in the sense of Thurston. First in § 2, we shall give a sufficient condition for the algebraic limit to coincide with the geometric limit. The statement is as follows.