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A finitely-presented solvable group with a small quasi-isometry group

Kevin Wortman
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Abstract

We exhibit a family of infinite, finitely-presented, nilpotent-by-abelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic Lie group. In addition, we propose a candidate for a polycyclic group whose quasi-isometry group is a solvable real Lie group, and we introduce a candidate for a quasi-isometrically rigid solvable group that is not finitely presented. We also record some conjectures on the large-scale geometry of lamplighter groups.

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Kevin Wortman. 2005-08-08. A finitely-presented solvable group with a small quasi-isometry group. https://arxiv.org/abs/math/0507191

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