A non-extended Hermitian form over \(\mathbb{Z}[\mathbb{Z}]\)
type: Item
instance of: scholarly article
title: A non-extended Hermitian form over \(\mathbb{Z}[\mathbb{Z}]\)
zbMATH Open document ID: 0890.57034
DOI: 10.1007/BF02677483
author: Ian Hambleton
author: Peter Teichner
published in: Manuscripta Mathematica
publication date: 1998-07-01T00:00:00Z
full work available at URL: https://eudml.org/doc/156311
review text: The authors describe a nonsingular Hermitian form of rank 4 over the group ring \(\mathbb{Z}[\mathbb{Z}]\) which is not extended from the integers. They also show that under certain indefiniteness assumptions, every nonsingular Hermitian form on a free \(\mathbb{Z}[\mathbb{Z}]\)-module is extended from the integers. Therefore there exists a closed oriented 4-dimensional manifold with fundamental group \(\mathbb{Z}\) which is not the connected sum of a simply connected 4-manifold and \(S^1\times S^3\).
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57N65
zbMATH DE Number: 1054313
zbMATH Keywords: Hermitian form
zbMATH Keywords: connected sum
reviewed by: Dušan Repovš
MaRDI profile type: Publication
cites work: Q4053793
cites work: Q4040346
cites work: Splitting 4-manifold with infinite cyclic fundamental group
cites work: Definite lattices over real algebraic function domains
description: scientific article; zbMATH DE number 1054313