The large scale geometry of some metabelian groups

2003/01/16 by J. Taback, Taback, J., K. Whyte +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.math/0301178

arxiv created 2003/01/16 · arxiv updated 2009/11/30

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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• The large scale geometry of the higher Baumslag-Solitar groups
• Large scale geometry of certain solvable groups
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• A finitely-presented solvable group with a small quasi-isometry group