Hyperbolic jigsaws and families of pseudomodular groups II

Autor:	Lou, Beicheng, Tan, Ser Peow, Vo, Anh Duc
Rok vydání:	2020
Předmět:	Mathematics - Geometric Topology Mathematics - Group Theory Mathematics - Number Theory 11F06 20H05 20H15 30F35 30F60 57M05 57M50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 32 pages, 7 figures, 5 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.10725 Zobrazit plný text záznamu View this record from Arxiv