Fake Schottky groups acting on the 3-sphere
type: Item
instance of: scholarly article
title: Fake Schottky groups acting on the 3-sphere
zbMATH Open document ID: 0876.30043
DOI: 10.1007/BF02104850
author: Nikolay Gusevskii
author: E. Ya. Klimenko
published in: Siberian Mathematical Journal
publication date: 1997-10-27T00:00:00Z
review text: A Kleinian group \(\Gamma\) on \(S^n, n\geq 2\), is said to be fake Schottky if \(\Gamma\) satisfies the following conditions: (A) \(\Gamma\) is a free group of finite rank; (B) \(\Gamma\) contains no parabolic elements; (C) \(\Gamma\) is geometrically finite; (D) \(\Gamma\) is not a Schottky group. The Schottky groups are well known to satisfy conditions (A) - (C). Bg virtue of the Maskit theorem the conditions (A) and (B) are necessary and sufficient for the group \(\Gamma\) to be Schottky in dimension \(n=2\). Hence fake Schottky groups are absent in dimension 2. In the present article a fake Schottky group acting on \(S^3\) is constructed.
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 1023944
zbMATH Keywords: Schottky groups
zbMATH Keywords: Kleinian groups
zbMATH Keywords: geometrically finite groups
zbMATH Keywords: parabolic elements
reviewed by: Alexander Mednykh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1023944