Volume 6, issue 2 (2006)

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A geometric proof that $\mathrm{SL}_2(\mathbb{Z}[t,t^{-1}])$ is not finitely presented

Kai-Uwe Bux and Kevin Wortman

Algebraic & Geometric Topology 6 (2006) 839–852
 arXiv: math.GR/0412101
Abstract

We give a new proof of the theorem of Krstić–McCool from the title. Our proof has potential applications to the study of finiteness properties of other subgroups of ${SL}_{2}$ resulting from rings of functions on curves.

Keywords
finiteness properties, trees, geometric group theory
Primary: 20F05
Secondary: 20F65