Classification of topological manifolds by the Euler characteristic and the \(K\)-theory ranks of \(C^\ast\)-algebras (Q2816157)
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scientific article; zbMATH DE number 6600431
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of topological manifolds by the Euler characteristic and the \(K\)-theory ranks of \(C^\ast\)-algebras |
scientific article; zbMATH DE number 6600431 |
Statements
1 July 2016
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\(K\)-theory
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\(C^\ast\)-algebra
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topological manifold
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Betti number
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Classification of topological manifolds by the Euler characteristic and the \(K\)-theory ranks of \(C^\ast\)-algebras (English)
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This article computes the \(K\)-theory of all two-dimensional manifolds and, more generally, higher-dimensional manifolds that can be obtained by taking a multiple connected sum of tori or of projective spaces, respectively. Then it is checked whether the ranks of the \(K\)-groups suffice to determine how many tori or projective spaces have been glued together. The main tool are long exact sequences. The paper closes with a definition of a connected sum of \(C^\ast\)-algebras.
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0.714848518371582
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0.6878294348716736
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