Riley 切片的逼近

The Riley slice revisited

In [4]: `The Riley slice of Schottky space', (Proc. London Math. Soc. 69 (1994), 72-90), Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of Schottky space R, the deformation space of a genus two handlebody generated by two parabolics. This theory aims to give a complete description of the deformation space of a holomorphic family of Kleinian groups in terms of the bending lamination of the convex hull boundary of the associated three manifold. In this note, we review the present status of the theory and discuss more carefully than in [4] the enumer…

A complex hyperbolic Riley slice

We study subgroups of ${\rm PU}(2,1)$ generated by two non-commuting unipotent maps $A$ and $B$ whose product $AB$ is also unipotent. We call $\mathcal{U}$ the set of conjugacy classes of such groups. We provide a set of coordinates on $\mathcal{U}$ that make it homeomorphic to $\mathbb{R}^2$ . By considering the action on complex hyperbolic space $\mathbf{H}^2_{\mathbb{C}}$ of groups in $\mathcal{U}$, we describe a two dimensional disc ${\mathcal Z}$ in $\mathcal{U}$ that parametrises a family of discrete groups. As a corollary, we give a proof of a conjecture of Schwartz for $(3,3,\infty)$-t…

双曲流形与折叠流形的单复维模空间

Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds

本文介绍了Riley slice及其背景，并将Keen和Series的工作扩展到同构于$\mathbb{Z}_p*\mathbb{Z}_q$的Kleinian群的单复维模空间。

Kleinian群由抛物线对生成的几何学

Geometry for Kleinian Groups Generated by a Parabolic Pair

本文提出了一种基于三角剖分的计算框架，用于研究由抛物线对生成的Kleinian群的双曲几何及2桥链接补集的结构。