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The large scale geometry of some metabelian groups

J. Taback·K. Whyte
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Abstract

We study the large scale geometry of the upper triangular subgroup of PSL(2,Z[1/n]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogues of the solvable Baumslag-Solitar groups BS(1,n).

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J. Taback, K. Whyte. 2003-01-16. The large scale geometry of some metabelian groups. https://arxiv.org/abs/math/0301178

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