The Farey Maps Modulo N

TL;DR

This paper investigates the structure of Farey maps modulo N, focusing on their quotients by principal congruence subgroups and the properties of their underlying graphs, contributing to the understanding of modular group actions on maps.

Contribution

It introduces a detailed analysis of Farey map quotients by principal congruence subgroups and explores their underlying graph structures, a novel approach in modular map theory.

Findings

Characterization of quotient maps by principal congruence subgroups

Analysis of the graph structures of these quotients

Insights into automorphism groups of Farey map quotients

Abstract

The Farey map is the universal triangular map whose automorphism group is the classical modular group. We study the quotients of the Farey map by the principal congruence subgroups of the modular group. We also study the structure of the underlying graphs of these quotients.