On the symmetries of the fake \({\mathbb{C}}P^ 2\) (Q1081902)
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scientific article; zbMATH DE number 3971793
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the symmetries of the fake \({\mathbb{C}}P^ 2\) |
scientific article; zbMATH DE number 3971793 |
Statements
On the symmetries of the fake \({\mathbb{C}}P^ 2\) (English)
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1986
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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 \textit{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).
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4-manifolds
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locally smoothable \({bbfZ}_ p\)-action on the Chern manifold
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homotopy equivalent to \({bbfC}P^ 2\)
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topological surgery theory
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