β Scribed by Alexander Zvonkin
No coin nor oath required. For personal study only.
A map is at the same time a group. To represent a map (that is, a graph drawn on the sphere or on another surface) we usually use a pair of permutations on the set of the 'ends' of edges. These permutations generate a group which we call a cartographic group. The main motivation for the study of the cartographic group is the so-called theory of 'dessins d'enfants' of Grothendieck, which relates the theory of maps to Galois theory [24].
In the present paper we address the questions of identifying the cartographic group for a given map, and of constructing the maps with a given cartographic group.
π SIMILAR VOLUMES
## Pictures of the Gz(2) hexagon and its dual are presented. A way to obtain these pictures is discussed.