Algebraic & Geometric Topology

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

Kevin P Knudson

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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].

Article information

Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2253-2261.

Received: 3 September 2008
Revised: 10 November 2008
Accepted: 13 November 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F05: Generators, relations, and presentations
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

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


Knudson, Kevin P. Homology and finiteness properties of $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$. Algebr. Geom. Topol. 8 (2008), no. 4, 2253--2261. doi:10.2140/agt.2008.8.2253.

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