On Klein–Schottky groups

Rubén A. Hidalgo and Bernard Maskit

Vol. 220 (2005), No. 2, 313–328

DOI: 10.2140/pjm.2005.220.313

Abstract

The retrosection theorem asserts that every closed Riemann surface of genus g ≥ 1 can be uniformized by a Schottky group of rank g. Here we define and topologically classify Klein–Schottky groups; these are the freely acting extended Kleinian groups whose orientation-preserving subgroup is a Schottky group. These groups yield uniformizations of all nonorientable closed Klein surfaces.

Keywords

Riemann surfaces, Klein surfaces, Schottky groups

Mathematical Subject Classification 2000

Primary: 30F10, 30F40

Milestones

Received: 16 May 2003

Revised: 29 October 2003

Accepted: 29 October 2003

Published: 1 June 2005