Spin bordism of oriented manifolds and the Hauptvermutung for 6-manifolds (Q2735123)
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scientific article; zbMATH DE number 1640126
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spin bordism of oriented manifolds and the Hauptvermutung for 6-manifolds |
scientific article; zbMATH DE number 1640126 |
Statements
17 January 2002
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simply connected 6-manifolds
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smooth classification
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topological classification
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spin bordism
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Spin bordism of oriented manifolds and the Hauptvermutung for 6-manifolds (English)
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The author gives a detailed proof of a part of classification results announced in 1988. The coincidence of the smooth and the topological classifications for closed simple connected smooth 6-manifolds is shown. More precisely, the main theorem is the following. Let \(M\) and \(M'\) be closed simply connected smooth 6-manifolds. Suppose that there exists a homeomorphism \(f : M \to M'\). Then there exists a diffeomorphism \(\varphi : M \to M'\) homologically identical to \(f\) (i.e., inducing the same isomorphisms \(H_i(M) \to H_i(M')\)).NEWLINENEWLINEFor the entire collection see [Zbl 0961.00011].
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