Caractéristiques d'Euler et groupes fondamentaux des variétés de dimension 4
type: Item
instance of: scholarly article
title: Caractéristiques d'Euler et groupes fondamentaux des variétés de dimension 4
zbMATH Open document ID: 0566.57011
DOI: 10.1007/BF02567405
author: Jean-Claude Hausmann
author: Shmuel Weinberger
published in: Commentarii Mathematici Helvetici
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140005
review text: Using a simple argument based on the multiplicative behaviour of the Euler characteristic with respect to a finite covering it is shown that if a 2-knot group has finite commutator subgroup T, then every abelian subgroup of T is cyclic (Theorem 5) and that there are finitely presentable superperfect groups which are not the fundamental groups of 4-dimensional homology spheres. (A result close to Theorem 5 was obtained by the reviewer [Bull. Aust. Math. Soc. 16, 449-462 (1977; Zbl 0352.57011)]. With regard to the closing problem of the article under review, it should be noted that \textit{C. M. Campbell} and \textit{E. F. Robertson} [Bull. Lond. Math. Soc. 12, 17-20 (1980; Zbl 0393.20020)] have shown that if p is a prime \(\geq 5\), then the finite group SL(2,p) has a presentation of deficiency 0; as it is superperfect it is the group of an homology 4-sphere.)
reviewed by: Jonathan A. Hillman
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 3903568
zbMATH Keywords: Euler characteristic
zbMATH Keywords: 2-knot group
zbMATH Keywords: commutator subgroup
zbMATH Keywords: finitely presentable superperfect groups
zbMATH Keywords: fundamental groups of 4-dimensional homology spheres
MaRDI profile type: Publication
OpenAlex ID: W1965240219
description: scientific article; zbMATH DE number 3903568