Classification of continuously transitive circle groups
Classification of continuously transitive circle groups
复制标题
连续传递圆群的分类
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
V. Marković
中科院分区：
文献类型：
--
作者：
James Giblin;V. Marković
设G是HOMO(S^1)的一个闭传递子群，它包含一条非常数的连续路径f：[0，1]→G.我们证明了直到共轭G是下列群之一：SO(2，ℝ)，PSL(2，ℝ)，PSL_k(2，ℝ)，HOMO_k(S^1)，HOMO(S^1).这验证了Ghys在[Enseign]中提出的分类。数学课。47(2001)329-407]。作为推论，我们证明了群Ps1(2，ℝ)是同上(S^1)的极大闭子群(我们理解这是De la Harpe的猜想)。我们还证明了如果这样的群G3，则G的闭包是同上的(S^1)(参看Bestvina的《几何群论中的问题集》)。
Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant continuous path f:[0,1]→G. We show that up to conjugation G is one of the following groups: SO(2,ℝ), PSL(2,ℝ), PSL_k(2,ℝ), Homeo_k(S^1), Homeo(S^1). This verifies the classification suggested by Ghys in [Enseign. Math. 47 (2001) 329-407]. As a corollary we show that the group PSL(2,ℝ) is a maximal closed subgroup of Homeo(S^1) (we understand this is a conjecture of de la Harpe). We also show that if such a group G 3, then the closure of G is Homeo(S^1) (cf Bestvina’s collection of ‘Questions in geometric group theory’)