A mixed version for a Fuchs' Lemma

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。

Flexibility of group actions on the circle

In this partly expository monograph we develop a general framework for producing uncountable families of exotic actions of certain classically studied groups acting on the circle. We show that if $L$ is a nontrivial limit group then the nonlinear representation variety $\mathrm{Hom}(L,\mathrm{Homeo}_+(S^1))$ contains uncountably many semi-conjugacy classes of faithful actions on $S^1$ with pairwise disjoint rotation spectra (except for $0$) such that each representation lifts to $\mathbb{R}$. For the case of most Fuchsian groups $L$, we prove further that this flexibility phenomenon occurs eve…