A proof of Kühnel's conjecture for \(n\geq k^ 2+3k\) (Q1359360)
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scientific article; zbMATH DE number 1029211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A proof of Kühnel's conjecture for \(n\geq k^ 2+3k\) |
scientific article; zbMATH DE number 1029211 |
Statements
A proof of Kühnel's conjecture for \(n\geq k^ 2+3k\) (English)
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6 May 1998
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The Kühnel's conjecture for combinatorial 2k-manifolds has been established by W. Kühnel and U. Brehm if the number \(n\) of vertices of M satisfies either \(n \leq 3k + 3\) or \(n \geq k^2 + 4k + 3\). In this paper, the author improves this result by showing that the conjecture is true for \(n \geq k^2 + 3 k\) and so he obtains as a corollary that the statement in the conjecture is true for \(k = 1\) and \(k = 2\).
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Kühnel's conjecture
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combinatorial manifold
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