## 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

### Keywords:

fake manifold; Gluck construction

Zbl 0564.57014
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