Two parabolic generator Kleinian groups
type: Item
instance of: scholarly article
title: Two parabolic generator Kleinian groups
zbMATH Open document ID: 0674.30035
DOI: 10.1007/BF02882422
author: Bernard Maskit
author: Gadde A. Swarup
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The main aim of the work under review is to prove that every torsion free Kleinian group G of the second kind generated by two parabolic transformations is geometrically finite (Theorem 1). The conclusion of this theorem fails if the assumption that G be of the second kind is dropped (Theorem 2). Normalizing G suitably it may be assumed without loss of generality that \(G=G_{\sigma}\) is generated by \[ A(z)=z+1\quad and\quad B(z)=B_{\sigma}(z)=z/(\sigma z+1). \] Then Theorem 3 says: The set of points \(\sigma\in {\mathbb{C}}\) for which \(G_{\sigma}\) is Kleinian of the second kind is path connected.
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 4103433
zbMATH Keywords: geometrically finite group
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02882422
OpenAlex ID: W2019757777
description: scientific article; zbMATH DE number 4103433