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Constructing a fake 4-manifold by Gluck construction to a standard 4- manifold. (English) Zbl 0649.57011

Let \(W=S\) 3\({\tilde \times}S\) 1#S \(2\times S\) 2 where the first summand is the twisted S 3 bundle over S 1. The author presents an imbedded 2-sphere S \(2\subseteq W\) and shows that the manifold M, obtained from W by the Gluck construction along S 2, is fake, i.e. M is simple homotopy equivalent but not diffeomorphic (or P.L. homeomorphic) to W. The same M was earlier constructed by the author in a different manner [Contemp. Math. 35, 75-141 (1984; Zbl 0564.57014)].
Reviewer: V.Turaev

MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57Q25 Comparison of PL-structures: classification, Hauptvermutung

Citations:

Zbl 0564.57014
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