Volume 8, issue 4 (2008)

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

Kevin P Knudson

Algebraic & Geometric Topology 8 (2008) 2253–2261
Abstract

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

Keywords
finite presentability, property $\mathrm{FP}_2$, linear groups over polynomial rings
Primary: 20F05
Secondary: 20F65