Linear groups - Malcev's theorem and Selberg's lemma

A note on Selberg's Lemma and negatively curved Hadamard manifolds

Answering a question by Margulis we prove that the conclusion of Selberg's Lemma fails for discrete isometry groups of negatively curved Hadamard manifolds.

一个定量的塞尔伯格引理

A Quantitative Selberg's Lemma

本文给出塞尔伯格引理的定量版本，证明半单李群中算术格的无挠子群指数在一般情况下为多项式、在广义黎曼假设下为多对数，并通过构造挠元素阶约为 log v / log log v 的格说明该界几乎最优。

关于 R. C. Alperin 一篇论文的注记

A note on a paper by R. C. Alperin

本文指出 R. C. Alperin 关于 Selberg 引理论文中推论 2 的陈述错误。

Controlling manifold covers of orbifolds

In this article we prove a generalization of Selberg's lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to questions of Long-Reid and the author.

带挠的Fuchsian群的分类

Classification of Fuchsian groups with torsion

本文证明了有限生成基本群的二维双曲orbifold的等距等价关系是可具体分类的，并利用该结果证明了具有非初等有限生成稳定子的非奇异遍历PSL_2(R)-空间是同质的。