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

TL;DR

This paper provides a structural decomposition theorem for extended ${ m Z}_{2n}$-Schottky groups, which are Kleinian groups associated with real points in Schottky space, using Klein-Maskit's combination theorems.

Contribution

It introduces a new structural decomposition theorem for extended ${ m Z}_{2n}$-Schottky groups based on Klein-Maskit's combination theorems.

Findings

Decomposition of extended ${ m Z}_{2n}$-Schottky groups into fundamental components.

Application of Klein-Maskit's combination theorems to these groups.

Enhanced understanding of the structure of real points in Schottky space.

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 $n \geq 1$. 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.