Classical Schottky groups of real type of genus two. I
type: Item
instance of: scholarly article
title: Classical Schottky groups of real type of genus two. I
zbMATH Open document ID: 0662.30044
author: Hiroki Sato
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: ``The boundary of the Schottky space consists of the boundary points due to Chuckrow, namely some discrete groups, and the boundary points due to Bers-Sato, namely points representing compact Riemann surfaces with nodes... In this paper we will consider a subspace of the classical Schottky space of genus two... and we will determine the structure of the boundary of the subspace. The space consists of all equivalence classes of marked classical Schottky groups generated by the following Möbius transformations \(A_ 1\) and \(A_ 2:\) \[ A_ jz=(a_ jz+b_ j)/(c_ jz+d_ j)\quad (a_ j,b_ j,c_ j,d_ j\in {\mathbb{R}},\quad a_ jd_ j-b_ jc_ j\neq 0;\quad j=1,2). \] We will divide the space into eight subspaces according to type (see {\S} 1). The space of the fourth type corresponds to the Teichmüller space for tori with a hole... In the first part, we will only consider the spaces of the first and fourth types...'' (From the introduction.)
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 4081934
zbMATH Keywords: boundary of the Schottky space
zbMATH Keywords: Schottky groups
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228077
OpenAlex ID: W1974263476
cites work: Automorphic forms for Schottky groups
cites work: On Schottky groups with applications to kleinian groups
cites work: Q4061209
cites work: The modular group and Riemann surfaces of genus two
cites work: Q4064258
cites work: Die Automorphismengruppe der freien Gruppen
cites work: On schottky-type groups with applications to riemann surfaces with nodes I
cites work: On schottky-type groups with applications to riemann surfaces with nodes II
cites work: On augmented Schottky spaces and automorphic forms, I
cites work: Introduction of new coordinates to the Schottky space. The general case
cites work: Augmented Schottky spaces and a uniformization of Riemann surfaces
cites work: Classical Schottky groups of real type of genus two. III
cites work: On a paper of Zarrow
cites work: Classical and non-classical Schottky groups
DOI: 10.2748/TMJ/1178228077
description: scientific article; zbMATH DE number 4081934