On 4-manifolds with universal covering space \(S^ 2\times R^ 2\) or \(S^ 3\times R\)
type: Item
instance of: scholarly article
title: On 4-manifolds with universal covering space \(S^ 2\times R^ 2\) or \(S^ 3\times R\)
zbMATH Open document ID: 0809.57010
DOI: 10.1016/0166-8641(93)90088-U
author: Jonathan A. Hillman
published in: Topology and its Applications
publication date: 1995-03-30T00:00:00Z
review text: The author sets out to characterise algebraically those closed connected 4-manifolds covered by either \(S^ 2 \times \mathbb{R}^ 2\) or \(S^ 3 \times \mathbb{R}^ 1\), and to bring the resulting manifolds into the geometric framework established by W. Thurston and C. T. C. Wall. In the first case one's model is an \(S^ 2\)-bundle over an aspherical surface, in the second a fibration over \(S^ 1\) with fibre an elliptic 3- manifold. These models do indeed tell a great deal of the story, which (subject to certain technical assumptions) is developed in the sequence: fundamental group \(\to\) homotopy type \(\to\) homeomorphism type using surgical methods. This works better in the first case than in the second, partly because of our continuing lack of a complete theory for 3- manifolds with finite fundamental group.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 447264
zbMATH Keywords: periodic cohomology
zbMATH Keywords: topological surgery
zbMATH Keywords: closed connected 4-manifolds covered by \(S^ 2 \times \mathbb{R}^ 2\) or \(S^ 3 \times \mathbb{R}^ 1\)
zbMATH Keywords: \(S^ 2\)-bundle over an aspherical surface
zbMATH Keywords: fibration over \(S^ 1\) with fibre an elliptic 3-manifold
reviewed by: Charles B. Thomas
MaRDI profile type: Publication
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Wikidata QID: Q125589098
description: scientific article; zbMATH DE number 447264