Regular coverings and parallel products of Farey maps

Abstract

We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel products, and use these observations to find their complete spectra, recovering some known results. We then examine a similar class of maps defined by Hecke groups.

Replaced November 2021. To be published in Acta Mathematica Universitatis Comenianae