论文标题
双曲线拼图和假导组的家族II
Hyperbolic jigsaws and families of pseudomodular groups II
论文作者
论文摘要
在上一篇论文中，我们引入了双曲线拼图构造，并构建了$ \ Mathrm {pslm {psl}（2，\ Mathbb {r}）$ cusp set $ \ mathbb {q} Q} \ cup \ cup \ fift pp \ aft pp \ aud pp，里德），因此回答了朗和里德提出的一个问题。在本文中，我们继续研究这些拼图群体，探讨了算术性，假导性的问题，以及相关的伪euclidean，并继续由这些群体引起的分数算法。我们还通过展示了递归的公式来回答另一个长期和里德的问题，该公式是由Weierstrass组引起的双曲线平面的镶嵌公式，该平面概述了用于产生Farey Tessellation的众所周知的“ Farey添加”。
In our previous paper, we introduced a hyperbolic jigsaw construction and constructed infinitely many non-commensurable, non-uniform, non-arithmetic lattices of $\mathrm{PSL}(2, \mathbb{R})$ with cusp set $\mathbb{Q} \cup \{\infty\}$ (called pseudomodular groups by Long and Reid), thus answering a question posed by Long and Reid. In this paper, we continue with our study of these jigsaw groups exploring questions of arithmeticity, pseudomodularity, and also related pseudo-euclidean and continued fraction algorithms arising from these groups. We also answer another question of Long and Reid by demonstrating a recursive formula for the tessellation of the hyperbolic plane arising from Weierstrass groups which generalizes the well-known "Farey addition" used to generate the Farey tessellation.
