论文标题
混凝土一个复合尺寸模量空间
Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds
论文作者
论文摘要
Riley Slice可以说是Kleinian群体模量空间的最简单例子。它自然地嵌入了$ \ mathbb {c} $中，并具有自然坐标系（由Linda Keen和Caroline系列在1990年代初引入），反映了基础3个manifold变形的几何形状。 Riley切片是在算术kleinian群体，两桥结，肖特基群体理论和双曲线3个manifolds理论的研究中产生的。由于其简单性，它提供了一个简单的示例和与这些主题相关的深层问题的来源。我们仅假设研究生水平的复杂分析和拓扑，向Riley Slice和许多相关背景材料提供了非专家的介绍。我们回顾围绕莱利片的历史和文学；然后我们宣布了自己的一些结果，将Keen和系列的工作扩展到了Kleinian组的一个复杂的维度模量空间，以$ \ MATHBB {Z} _P*\ MATHBB {Z} _Q $在Riemann Sphere上作用于Riemann Sphere上，$ 2 \ leq P，Q \ leq p，q \ le q \ soumq \ sovty。 Riley Slice就是$ p = q = \ infty $（即两个抛物线发电机）。
The Riley slice is arguably the simplest example of a moduli space of Kleinian groups; it is naturally embedded in $ \mathbb{C} $, and has a natural coordinate system (introduced by Linda Keen and Caroline Series in the early 1990s) which reflects the geometry of the underlying 3-manifold deformations. The Riley slice arises in the study of arithmetic Kleinian groups, the theory of two-bridge knots, the theory of Schottky groups, and the theory of hyperbolic 3-manifolds; because of its simplicity it provides an easy source of examples and deep questions related to these subjects. We give an introduction for the non-expert to the Riley slice and much of the related background material, assuming only graduate level complex analysis and topology; we review the history of and literature surrounding the Riley slice; and we announce some results of our own, extending the work of Keen and Series to the one complex dimensional moduli spaces of Kleinian groups isomorphic to $\mathbb{Z}_p*\mathbb{Z}_q$ acting on the Riemann sphere, $2\leq p,q \leq \infty$. The Riley slice is the case $p=q=\infty$ (i.e. two parabolic generators).
