Homology and finiteness properties of \(\text{SL}_2(\mathbb{Z}[t,t^{-1}])\). (Q1007189)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homology and finiteness properties of \(\text{SL}_2(\mathbb{Z}[t,t^{-1}])\). |
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Homology and finiteness properties of \(\text{SL}_2(\mathbb{Z}[t,t^{-1}])\). (English)
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20 March 2009
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It is unknown whether the group \(G=\text{SL}_2(\mathbb{Z}[t,1/t])\) is generated by elementary matrices. Bux and Wortman proved that \(G\) is not finitely presented. In the present paper the following stronger result is obtained: \(H_2(G)\) is not finitely generated. The author suspects that the same is true for the higher homology groups of \(G\).
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finite presentations
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homology groups
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\(FP_2\) property
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linear groups over polynomial rings
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