|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Hyperbolic jigsaws and
families of pseudomodular groups, I
Beicheng Lou, Ser Peow Tan and Anh Duc Vo |
|
Geometry & Topology 22 (2018) 2339–2366
|
Abstract |
|
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. |
Keywords
pseudomodular, killer intervals, hyperbolic jigsaw, marked
ideal triangle
|
Mathematical Subject Classification 2010
Primary: 11F06, 20H05, 20H15, 30F35, 30F60
Secondary: 57M05, 57M50
|
References |
Publication
Received: 15 November 2016
Revised: 23 June 2017
Accepted: 9 October 2017
Published: 5 April 2018
Proposed: Ian Agol
Seconded: Anna Wienhard, Jean-Pierre Otal
|
Authors |
| Beicheng Lou | |
| Department of Mathematics National University of Singapore Singapore |
|
| Ser Peow Tan | |
| Department of Mathematics National University of Singapore Singapore |
|
| http://www.math.nus.edu.sg/~mattansp/ | |
| Anh Duc Vo | |
| Department of Mathematics National University of Singapore Singapore |
|
