turkmath.org

In this talk, notions of suborbital graphs and regular maps are presented. The connection between a graph and a regular map is introduced. First we present the results regarding the suborbital graphs for the normalizer $\Gamma_B (N)$ of $\Gamma_0 (N)$ in $PSL(2,\mathbb{R})$, where the normalizer is a triangle group. Then the regular maps corresponding to the subgroups $Γ_0 (N)$ of the modular group is investigated. The method given in this talk consists of finding an appropriate chain of subgroups of $\Gamma_B (N)$, and relating these subgroups with the structure of the associated regular maps.