On the lower nil-groups of Waldhausen (Q2703555)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the lower nil-groups of Waldhausen |
scientific article |
Statements
7 March 2001
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\(K\)-theory
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nil-groups of Waldhausen
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amalgamated free product
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vanishing conjecture of lower \(K\)-groups
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HNN-extensions of groups
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On the lower nil-groups of Waldhausen (English)
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Let \(\Gamma= \Gamma_0 *_G \Gamma_1\) be an amalgamated free product, where \(G\) is a finitely generated central subgroup of \(\Gamma_0\) and \(\Gamma_1\). The authors of this paper prove that the negative Waldhausen nil-groups that appear in the calculation of the \(K\)-theory of \({\mathbb Z}\Gamma\) vanish. Some applications are obtained for the vanishing conjecture of lower \(K\)-groups. The methods developed in this paper also work for HNN-extensions of groups.
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