A geometric proof that SL2(ℤ[t,t−1]) is not finitely presented

Bux, Kai-Uwe; Wortman, Kevin

doi:10.2140/agt.2006.6.839

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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

DOI: 10.2140/agt.2006.6.839

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

Mathematical Subject Classification 2000

Primary: 20F05

Secondary: 20F65

References

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Publication

Received: 15 December 2004

Revised: 11 April 2006

Accepted: 28 October 2005

Published: 11 July 2006

Authors

Kai-Uwe Bux
Department of Mathematics University of Virginia PO Box 400137 Charlottesville VA 22094-4137 USA

Kevin Wortman
Mathematics Department Yale University PO Box 208283 New Haven CT 06520-8283 USA

Volume 6, issue 2 (2006)