Hyperbolic jigsaws and families of pseudomodular groups I

Autor:	Lou, Beicheng, Tan, Ser Peow, Vo, Anh Duc
Rok vydání:	2016
Předmět:	Mathematics - Geometric Topology Mathematics - Group Theory Mathematics - Number Theory 11F06 20H05 20H15 30F35 30F60 57M05 57M50
Zdroj:	Geom. Topol. 22 (2018) 2339-2366
Druh dokumentu:	Working Paper
DOI:	10.2140/gt.2018.22.2339
Popis:	We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to the modular group. We do this by introducing a general construction for the fundamental domains of Fuchsian groups obtained by gluing together marked ideal triangular tiles, which we call hyperbolic jigsaw groups. Comment: 21 pages, 4 figures, comments welcomed. Section 8 rewritten with a stronger result. Minor corrections to other parts. Grant acknowledgement added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1611.02922 Zobrazit plný text záznamu View this record from Arxiv