2020/07/03 by Hidalgo, Rubén A.
#30F10 #30F40 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2007.01781
Let (S,η) be an origami pair, that is, S is a closed Riemann surface of genus g ≥1 and η:S → E is a holomorphic branched covering, with at most one branch value, where E is a genus one Riemann surface. As the lowest uniformizations of S are provided by Schottky groups, we are interested in describing origami pairs in terms of virtual Schottky groups. In other words, we are interested in those Kleinian groups K which contain, as a finite index subgroup, a Schottky group Γ such that S=Ω/Γ and such that η is induced by the inclusion Γ≤ K. We say that K is an origami-Schottky group. We provide a geometrical structural picture, in terms of the Klein-Maskit combination theorems, of these origami-Schottky groups.