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arXiv · 1910.03050

Modular groups and planar maps

Abdellah Sebbar·Khalil Besrour
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Abstract

In this paper 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.

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Abdellah Sebbar, Khalil Besrour. 2019-10-07. Modular groups and planar maps. https://arxiv.org/abs/1910.03050

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