Counterexamples to the Kneser conjecture in dimension four
type: Item
instance of: scholarly article
title: Counterexamples to the Kneser conjecture in dimension four
zbMATH Open document ID: 0837.57016
DOI: 10.1007/BF02566016
author: Wolfgang Lück
author: Matthias Kreck
author: Peter Teichner
published in: Commentarii Mathematici Helvetici
publication date: 1996-01-28T00:00:00Z
full work available at URL: https://eudml.org/doc/140377
review text: First some examples are given of closed smooth orientable 4-manifolds \(M\) whose fundamental group splits as a nontrivial free product, but such that if \(M\) is homotopy equivalent to the connected sum \(M_0 \# M_1\), then \(M_0\) or \(M_1\) is homeomorphic to \(S^4\). An example is then given of a closed smooth orientable 4-manifold \(M\) which is homeomorphic to \(M_0 \# M_1\), these being closed topological 4- manifolds, each with fundamental group cyclic of order two, but such that \(M \# k(S^2 \times S^2)\) is diffeomorphic to \(M_0 \# M_1\) for non-simply-connected smooth 4-manifolds \(M_0\) and \(M_1\) if and only if \(k \geq 8\).
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 838579
zbMATH Keywords: 4-manifolds
zbMATH Keywords: fundamental group
Wikidata QID: Q123115503
reviewed by: C. Kearton
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 838579