A structural description of extended ${\mathbb{Z}}_{2n}$-Schottky groups

Abstract

Real points of Schottky space ${\mathcal{S}}_g$ are in correspondence with extended Kleinian groups $K$ containing, as a normal subgroup, a Schottky group $\Gamma$ of rank $g$ such that $K/\Gamma \cong {\mathbb{Z}}_{2n}$ for a suitable integer $n\ge 1$. These kind of groups are called extended ${\mathbb{Z}}_{2n}$-Schottky groups of rank $g$. In this paper, we provide a structural decomposition theorem, in terms of Klein-Maskit's combination theorems, of these kind of groups.