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On the symmetries of the fake \({\mathbb{C}}P^ 2\). (English) Zbl 0602.57027
The author shows that for each odd prime p there is a locally smoothable \({\mathbb{Z}}_ p\)-action on the Chern manifold Ch (which is homotopy equivalent to \({\mathbb{C}}P^ 2\) but admits no smooth structure). This is in so far interesting as he had shown in joint work with P. Vogel that no such action exists for \(p=2\) [Asymmetric 4-dimensional manifolds, Duke Math. J. 53, 759-764 (1986)]. The proof uses standard techniques from topological surgery theory (which can be applied to dimension 4 by Freedman’s work).
Reviewer: M.Krech

MSC:
57S25 Groups acting on specific manifolds
57S17 Finite transformation groups
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
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References:
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[2] Freedman, M., Quinn, F.: Topology of 4-manifolds. Ann. Math. Studies (to appear) · Zbl 0705.57001
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