A construction of certain 3-manifolds with orientation reversing involution
type: Item
instance of: scholarly article
title: A construction of certain 3-manifolds with orientation reversing involution
zbMATH Open document ID: 0637.57026
author: Masako Kobayashi
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: In the reviewer's paper ``On 3-manifolds admitting orientation-reversing involutions'' [ibid. 33, 571-589 (1981; Zbl 0474.57006)], it is observed that the first homology group of a closed orientable 3-manifold with an orientation reversing involution has the torsion part of a direct double or a direct sum of a direct double and the group of order two. Further, it is shown that any finitely generated Abelian group with torsion part a direct double is realizable by an irreducible one, but if the whole group is a direct sum of a direct double of odd order (\(\neq 1)\) and the group of order two, then it is not realizable by any irreducible one. In this paper, the author proves by a concrete construction that any finitely generated Abelian group except for this special case is realizable by an irreducible one if its torsion part is a direct double or a direct sum of a direct double and the group of order two.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 4038828
zbMATH Keywords: fixed point set
zbMATH Keywords: 3-manifolds admitting orientation-reversing involutions
zbMATH Keywords: first homology group
zbMATH Keywords: finitely generated Abelian group
zbMATH Keywords: torsion part
zbMATH Keywords: direct double
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04010151
OpenAlex ID: W2031863486
DOI: 10.2969/JMSJ/04010151
description: scientific article; zbMATH DE number 4038828