Geometric decomposition of spatial Kleinian groups and fundamental groups of 3-manifolds
type: Item
instance of: scholarly article
title: Geometric decomposition of spatial Kleinian groups and fundamental groups of 3-manifolds
zbMATH Open document ID: 0696.57003
DOI: 10.1007/BF00971270
author: L. D. Potyagajlo
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let G be a finitely generated group of Möbius transformations of the 3- dimensional Möbius space \({\mathbb{R}}^ 3\cup \{\infty \}\). Suppose that G is a functional Kleinian group and that G acts freely on an invariant component \(\Omega\). Let \(M=\Omega /G\). Suppose further that G is isomorphic to the fundamental group of a Haken manifold with toroidal boundary. Under these assumptions the author proves that every decomposition \(G=G_ 1*_{G_ 2}G_ 3\) or \(G=G_ 1*_{G_ 2}\) can be realized by an incompressible surface in M. This extends some work of Maskit.
Mathematics Subject Classification ID: 57M99
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 4140830
zbMATH Keywords: free product decomposition of groups
zbMATH Keywords: Möbius transformations
zbMATH Keywords: Möbius space
zbMATH Keywords: invariant component
zbMATH Keywords: fundamental group
zbMATH Keywords: Haken manifold
zbMATH Keywords: incompressible surface
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00971270
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description: scientific article; zbMATH DE number 4140830