Type: Article

On the topology of infinite regular and chiral maps

Arredondo, J. A; Maluendas, C. R; Valdez, F.;

Abstract:

We prove that infinite regular and chiral maps can only exist on surfaces with one end. Moreover, we prove that an infinite regular or chiral map on an orientable surface with positive genus, can only be realized on the Loch Ness monster, that is, the topological surface of infinite genus with one end