Translator Disclaimer
October 2021 Modular groups and planar maps
Abdellah Sebbar, Khalil Besrour
Rocky Mountain J. Math. 51(5): 1847-1863 (October 2021). DOI: 10.1216/rmj.2021.51.1847

Abstract

We give an explicit formula for the number of subgroups of the modular group of a given index that are genus zero and torsion-free, and a formula for their conjugacy classes. We do so by exhibiting a correspondence between these groups and the trivalent maps on a sphere. We focus on the particular case of the subgroups of index 18 which have some interesting geometric properties.

Citation

Download Citation

Abdellah Sebbar. Khalil Besrour. "Modular groups and planar maps." Rocky Mountain J. Math. 51 (5) 1847 - 1863, October 2021. https://doi.org/10.1216/rmj.2021.51.1847

Information

Received: 11 October 2019; Revised: 9 March 2021; Accepted: 9 March 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1847

Subjects:
Primary: 05C30 , 11F06

Keywords: K3 surfaces , modular group , noncongruence subgroups , planar maps

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.51 • No. 5 • October 2021
Back to Top