Strong Tits alternatives for compact 3-manifolds with boundary
type: Item
instance of: scholarly article
title: Strong Tits alternatives for compact 3-manifolds with boundary
zbMATH Open document ID: 1056.57001
published in: Journal of Pure and Applied Algebra
publication date: 2004-08-19T00:00:00Z
review text: Es gibt verschiedene Eigenschaften, aufgrund derer man eine unendliche Gruppe \(G\) ``groß'' nennt. Eine solche ist, dass \(G\) die freie Gruppe \(F_2\) vom Rang 2 als Untergruppe besitzt. Die vorliegende Arbeit untersucht 3-Mannigfaltigkeitsgruppen auf diese Eigenschaften. Das Haupt\-resultat ist, dass eine für kompakte, orientierbare, irreduzible 3-Mannigfaltigkeit mit nichtleerem Rand \(\pi_1\) entweder virtuell abelsch ist oder eine Untergruppe von endlichem Index enthält, welche \(F_2\) als Quotient zulässt. Wenn die Randkomponenten nicht nur aus Sphären oder projektiven Ebenen bestehen, kann man eine Ab\-schwä\-chung (``Semi-Tits-Alternative'') auch ohne die Forderung der Irreduzibilität beweisen.
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 2093440
zbMATH Keywords: large groups
zbMATH Keywords: 3-manifold groups
author: Jack Button
reviewed by: Karlheinz Knapp
MaRDI profile type: Publication
full work available at URL: j.jpaa.2003.12.009
OpenAlex ID: W1969599231
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DOI: 10.1016/J.JPAA.2003.12.009
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description: scientific article; zbMATH DE number 2093440