Homology and finiteness properties of $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$

Kevin P Knudson

doi:10.2140/agt.2008.8.2253

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Home > Journals > Algebr. Geom. Topol. > Volume 8 > Issue 4 > Article

2008 Homology and finiteness properties of $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$

Kevin P Knudson

Algebr. Geom. Topol. 8(4): 2253-2261 (2008). DOI: 10.2140/agt.2008.8.2253

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Abstract

We show that the group $H_{2} ({SL}_{2} (ℤ [t, t^{- 1}]); ℤ)$ is not finitely generated, answering a question mentioned by Bux and Wortman in [Algebr. Geom. Topol. 6 (2006) 839-852].

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Kevin P Knudson. "Homology and finiteness properties of $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$." Algebr. Geom. Topol. 8 (4) 2253 - 2261, 2008. https://doi.org/10.2140/agt.2008.8.2253

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Received: 3 September 2008; Revised: 10 November 2008; Accepted: 13 November 2008; Published: 2008

First available in Project Euclid: 20 December 2017

zbMATH: 1167.20026

MathSciNet: MR2465740

Digital Object Identifier: 10.2140/agt.2008.8.2253

Subjects:

Primary: 20F05

Secondary: 20F65

Keywords: finite presentability , linear groups over polynomial rings , property $\mathrm{FP}_2$

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Kevin P Knudson "Homology and finiteness properties of $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$," Algebraic & Geometric Topology, Algebr. Geom. Topol. 8(4), 2253-2261, (2008)

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