Homology and finiteness properties of SL2(ℤ[t,t−1])

Knudson, Kevin P

doi:10.2140/agt.2008.8.2253

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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

DOI: 10.2140/agt.2008.8.2253

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].

Keywords

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

Mathematical Subject Classification 2000

Primary: 20F05

Secondary: 20F65

References

Publication

Received: 3 September 2008

Revised: 10 November 2008

Accepted: 13 November 2008

Published: 11 December 2008

Authors

Kevin P Knudson
Department of Mathematics & Statistics Mississippi State University Mississippi State, MS 39762 USA
http://www2.msstate.edu/~kk116/

Volume 8, issue 4 (2008)