Seifert fibre spaces and Poincaré duality groups
type: Item
instance of: scholarly article
title: Seifert fibre spaces and Poincaré duality groups
zbMATH Open document ID: 0554.57011
DOI: 10.1007/BF01215136
author: Jonathan A. Hillman
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173631
review text: We show that a Poincaré duality group of formal dimension three which has a subgroup of finite index with infinite abelianization and containing a nontrivial abelian normal subgroup is the fundamental group of a closed 3-manifold which is Seifert fibred or admits a Sol-structure. (With some obvious exceptions these algebraic conditions are satisfied by the groups of all such manifolds.) We give a corresponding characterization for the groups of bounded Seifert fibre spaces.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57P10
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 3883215
zbMATH Keywords: Poincaré duality group of formal dimension three
zbMATH Keywords: nontrivial abelian normal subgroup
zbMATH Keywords: fundamental group of a closed 3-manifold
zbMATH Keywords: Sol-structure
zbMATH Keywords: Seifert fibre spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3883215