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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 H2(SL2([t,t1]); ) 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/